L0ckAndL0ad

Yes, lots of suppressive fire.  After that, in the game, some players report that it's effective to SLOW move into the building.  If enemy is still not spotted by an adjacent to the building unit, I generally QUICK move in.  If you HUNT the unit could get fired upon and get "stuck".
The biggest challenge I have faced is when the enemy are not in the building but behind a far wall.  So, one's unit enters the deserted building, then gets mowed down by enemy hiding behind a wall on the far side.  Smoke may help. 
Otherwise I have learned to have them enter the building on QUICK and immediately FAST move back out the same way they entered.  That way they can "recon" the interior and far wall, but don't stay to be massacred during the minute you can't issue new orders (in WEGO am talking about obviously).   
One can also use PAUSE so that they unit enters the building only in the last few seconds of a WEGO turn.  That way they may spot the enemy first and can fire at the far wall immediately at the start of the next WEGO turn.

You summed it up @L0ckAndL0ad along with what @Chudacabra said the only thing to add is breach from a location that does not have a door. Sometimes you can do that form an adjacent building too which is even more fun because then you can do it from an upper floor.

For fun - this is @slysniper's men doing just that to my guys:
 

*Takes Bow*
 
I am "Brian" in this particular episode.   I "star" in three others from this season.   Speak to my agent for interviews.   :)
Full disclosure, I am not a veteran of Iraq II.  My time was before 2003/2004.  

Sitrep @ 9:22
1st Platoon, slowly but surely, moves forward to secure Obj Drake. Resupply is almost complete, though not without some quirks.
2nd Platoon got a new casualty the moment the first element reached the outer fence of Obj Morty compound... Nothing I can do about it.
The route for 3rd Platoon's movement is still not secure enough, so I wait before committing them.
LAR Platoon is on the move. I spread everyone out along the northern front, leapfrogging forward. Also ordered the LAV-25 crews to stick their heads out for a bit to check out the surroundings. The northern flank presents a dilemma. On the one hand, there's ~80% flat terrain, more suitable for mounted forces, and making dismounted recon elements very vulnerable. On the other hand, there are ditches and tree lines capable of hiding enemy infantry and AT assets. The ideal solution would be using LAVs on flat terrain while sending dismounts over ditches and tree lines, but that's not always possible due to some unique terrain features. So yeah, I kinda struggle to advance as quickly as I anticipated.
Scout Snipers have reached the Point 37 near Hill 42 (SE corner of the map). I'm not 100% sure if I should send them further north to the low ground area, or keep them at Point 37 hill where they'd have better overview of the area.
Enemy HQ combatant at Obj Vasquez managed to survive the Javelin strike! The fella lying next to him is supposedly the RPG-29 gunner.

2nd Platoon's being hit:

LAR Platoon leapfrogs eastbound on the northern flank:

Sitrep @ 9:19
I've got two Javelin teams placed strategically at high ground in order to be able to quickly hit High Value Targets as they appear (also for better spotting). The room that the RPG-29 gunner appeared the last time in is the same room an enemy HQ combatant have run towards/into. So I ordered an immediate attack on that room with a Javelin missile. The room has collapsed. In other news, 1st Platoon got another casualty during resupply... 2nd Platoon is still facing opposition in the first line of houses near the trenches but is ready to move into Obj Morty any minute now.
Enemy HQ spotted @ Obj Vasquez:

2nd Platoon receives fire from the buildings @ Obj Morty:

Javelin attack on enemy HQ & RPG-29 position:

1st Platoon is trying to resupply during combat, but can't find a better place for it. There's a large ditch on the left side of the road, and no way to drive into the alleys on the right side. So the resupply has to be done right in the middle of the street.
 

Sitrep @ 9:16
Hmmm. I've got 45 minutes until the time runs out. This is that phase I'm sure many of us have experienced when you think you're not making in it in time and rush things, making it worse for yourself. I kinda have to deploy 3rd Platoon to its objective areas ASAP. But the direct route there isn't cleared yet. What do I do? This is the route I think might be relatively safe:

LAR's LAV-25s roll over Hill 55 to support 1st Platoon:

LAVs level the building with the RPG guy inside:

RPG-29 dude @ Obj Vasquez is out again to ruin my Marines' day:

Yes, indeed.
Sitrep @ 9:13
I'll keep it short and let the screenies talk.
LAR dismounts kill 2 out of visible 3 enemy SF FO team (hand grenades FTW!):

1st Platoon's positions: fighting in the streets, flanking fire by LAV-25s onto hit&run RPG guy, one of the fireteams resupplies from the amtrack:



Most of the 2nd Platoon is in the trenches by now. And we've got some enemy HQ pinned down @ Obj Morty:

Sitrep @ 9:12
Oh my.. Now the real chaos of war starts. LAR dismounts uncovered enemy special forces FO. 1st Platoon is in firefight against some AK & RPG dudes who do hit & run in the alleys. Fortunately, LAV-25s are there to fire on the northern flank.
But the real meat of this story is with the 2nd Platoon. They got an RPG in their faces (after my semi-failed smokescreen rush) and uncovered SIX enemy teams, 4 on Obj Morty, two in the trenches. The ones in the trenches are dead by now (I think...). But the guys in the buildings & on rooftops are harder to target due to all the smoke..
LAR & enemy FO encounter:

Chaos of war: 2nd Platoon edition

Sitrep @ 9:19
I've got two Javelin teams placed strategically at high ground in order to be able to quickly hit High Value Targets as they appear (also for better spotting). The room that the RPG-29 gunner appeared the last time in is the same room an enemy HQ combatant have run towards/into. So I ordered an immediate attack on that room with a Javelin missile. The room has collapsed. In other news, 1st Platoon got another casualty during resupply... 2nd Platoon is still facing opposition in the first line of houses near the trenches but is ready to move into Obj Morty any minute now.
Enemy HQ spotted @ Obj Vasquez:

2nd Platoon receives fire from the buildings @ Obj Morty:

Javelin attack on enemy HQ & RPG-29 position:

1st Platoon is trying to resupply during combat, but can't find a better place for it. There's a large ditch on the left side of the road, and no way to drive into the alleys on the right side. So the resupply has to be done right in the middle of the street.
 

Sitrep @ 9:22
1st Platoon, slowly but surely, moves forward to secure Obj Drake. Resupply is almost complete, though not without some quirks.
2nd Platoon got a new casualty the moment the first element reached the outer fence of Obj Morty compound... Nothing I can do about it.
The route for 3rd Platoon's movement is still not secure enough, so I wait before committing them.
LAR Platoon is on the move. I spread everyone out along the northern front, leapfrogging forward. Also ordered the LAV-25 crews to stick their heads out for a bit to check out the surroundings. The northern flank presents a dilemma. On the one hand, there's ~80% flat terrain, more suitable for mounted forces, and making dismounted recon elements very vulnerable. On the other hand, there are ditches and tree lines capable of hiding enemy infantry and AT assets. The ideal solution would be using LAVs on flat terrain while sending dismounts over ditches and tree lines, but that's not always possible due to some unique terrain features. So yeah, I kinda struggle to advance as quickly as I anticipated.
Scout Snipers have reached the Point 37 near Hill 42 (SE corner of the map). I'm not 100% sure if I should send them further north to the low ground area, or keep them at Point 37 hill where they'd have better overview of the area.
Enemy HQ combatant at Obj Vasquez managed to survive the Javelin strike! The fella lying next to him is supposedly the RPG-29 gunner.

2nd Platoon's being hit:

LAR Platoon leapfrogs eastbound on the northern flank:

In very rare cases, you can even use snipers at the sharp end.
Time-stamped below is an example of such:
Their position on the third roof of a multi-building complex kept them relatively safe from enemy fire, and aside from cowering a few times, they were free to fire upon the enemy for the duration of the battle. Their position and fire stopped an enemy attack long enough for me to divert additional assets to deal with it.

Try to allow them to fire at close to their maximum range, and ensure they are in cover when firing (building, or woods) and better, under cover in a key hole position.  That should help, but yeah, they are a challenge to use effectively.  I also struggle with them.  Good luck.
Bil

Sitrep @ 9:16
Hmmm. I've got 45 minutes until the time runs out. This is that phase I'm sure many of us have experienced when you think you're not making in it in time and rush things, making it worse for yourself. I kinda have to deploy 3rd Platoon to its objective areas ASAP. But the direct route there isn't cleared yet. What do I do? This is the route I think might be relatively safe:

LAR's LAV-25s roll over Hill 55 to support 1st Platoon:

LAVs level the building with the RPG guy inside:

RPG-29 dude @ Obj Vasquez is out again to ruin my Marines' day:

I have seen that kind of thing before in buildings - changing the face command ends up being ignored for some reason. If you give them a move order to the same floor and put the face command on that end point it will work more consistently.

Below is my pop smoke drill for infantry.  I always give a Face command to make sure of the direction of the throw. 
1. Check wind direction & strength1.
2. Position throwing team so the 20 meter thrown grenade lands where needed.
3. On the turn of the throw don't move the unit popping the smoke (Team “A”).
4. Give team “A” a Face command in the direction you want the smoke thrown.
5. With team “A” still selected, choose the Pop Smoke command.
6. Next turn, Fast the moving team across area (If Quick they may stop to shoot).
Notes: Smoke grenades, thrown by one team, can reliably obscure up to 3 A/S (24 meters). Smoke (not frag) hand grenades are automatically thrown 20 meters by the AI (three action spots).   1) Wind strength not more than medium.

I've posted Combat Mission on Pornhub. No one can stop me.

Yep, Drake & Vasquez are Colonial Marines from the Aliens. Rick & Morty are pretty obvious characters. But who can guess the last two? What are these here? 🎷 📷 🔦 
Sitrep @ 9:06
I came up with the spreadsheet to calculate and track headcounts. Somewhat late, but whatever.
https://docs.google.com/spreadsheets/d/1ngebYsppFeg7-qoZhZVVLf_Z49xL7rsBsCtPEqTNiA0/edit?usp=sharing
1st Platoon is at 62% manpower. 2nd and 3rd are at 96%. Total headcount is at 84%. Vehicles are fine, minus just two heavy weapons humvees so far.
LAR's LAVs shift to Hill 55 BOF position:

Overview of the 1st Platoon's position and surroundings:

Obj Drake is pretty straightforward. Elements do consecutive moves on both sides of the road, covering each other. Outside help from LAV-25s and AAVs pours in 25mm, 40mm and M2 fire when needed, also providing flank security:

Getting onto Vasquez's 4th base would be hard. 1st Platoon's Assault team survivors (two Marines) still got some explosives, so going into the front door can be avoided. Can also get help from the 2nd Platoon for this. Anyone got any ideas?

Thank you for your support, people! I really appreciate it!
Tactical situation & plans
Mkay, I'm gonna get a little creative here. Bonus points to people who can guess all the references. I came up with a couple of defined objective areas I need to clear to complete my mission.
1st Platoon is barely hanging in there. It's low on ammo and manpower. But there are two areas I need them to clear. Obj Drake is the rest of the village up until the Bridge 003, minus the separate badass walled compound where the RPG-29 guy is currently residing (that's Obj Vasquez). 
2nd Platoon is in good shape, with only one squad being currently engaged in the trenches. As soon as mortar fire mission is over, I'll get the smoke screen up and let Marines rush to the nearest compound (Obj Morty). Getting to Obj Rick would be their next move.
3rd Platoon is still in Reserve and will be tasked with clearing Obj Phelps & Jones. The situation there is a complete mystery (hint hint) to me. Someone'd have to investigate the safest & quickest route for AAVs to use so I could drop the Marines off as close as possible (probably the main road aka Route Major).
Scout Snipers & LAR Platoon will keep scouting the flanks, southern and northern respectively. 
That's it for now.

Thank you for your support, people! I really appreciate it!
Tactical situation & plans
Mkay, I'm gonna get a little creative here. Bonus points to people who can guess all the references. I came up with a couple of defined objective areas I need to clear to complete my mission.
1st Platoon is barely hanging in there. It's low on ammo and manpower. But there are two areas I need them to clear. Obj Drake is the rest of the village up until the Bridge 003, minus the separate badass walled compound where the RPG-29 guy is currently residing (that's Obj Vasquez). 
2nd Platoon is in good shape, with only one squad being currently engaged in the trenches. As soon as mortar fire mission is over, I'll get the smoke screen up and let Marines rush to the nearest compound (Obj Morty). Getting to Obj Rick would be their next move.
3rd Platoon is still in Reserve and will be tasked with clearing Obj Phelps & Jones. The situation there is a complete mystery (hint hint) to me. Someone'd have to investigate the safest & quickest route for AAVs to use so I could drop the Marines off as close as possible (probably the main road aka Route Major).
Scout Snipers & LAR Platoon will keep scouting the flanks, southern and northern respectively. 
That's it for now.

Sitrep @ 9:03
Who gets more casualties? 1st Platoon gets more casualties. What a shock. Well, actually, RPG-29 team popped up on one of the buildings and made a big bada boom into my Marines' faces. RPG dude ran off fast, so there's little point shooting at that building. But I ordered some area fire and AH-1 Cobra strike on it anyway, just in case. There haven't been many of those so far, so why not.
RPG-29 hit:

RPG-29 location (duh):

2nd Platoon's AAVs were ordered back and high up the hills, to get better firing solutions.

Marketing is not Battlefront's strongest point. ChrisND's Twitch streams were great and are sorely missed.

He admires my muscle control.
 
Mord.

Artkin, if this is how you speak in real life I would murder you after one conversation. LOL. I haven't been this confused since my proctologist sent me flowers and a Thank You card.
 
Mord.

I used to have FRAPs for this, but I don't have it now. These days I use Steam. You can import any game into it, very easy. Then launch the game from the Steam (or create a new shortcut from inside the Steam) and Steam overlay will hook up and screenshot function will work inside the game.
One major note though! There's a hotkey conflict. I had to set Steam screenshots to F1 instead of the default one which is used in CM.
Result: https://steamcommunity.com/profiles/76561198004245883/screenshots/?appid=sc_107807&sort=newestfirst&browsefilter=myfiles&view=grid