I'm a new player and have had problems with the difficulty as well.
I think the best advice I've read on this thread is to play with the quick battle system. Scenarios and campaigns are generally made by experienced players for experienced players, and can be brutal for the newbie. Even if you don't want to pick both sides yourself, you can still adjust the force levels to give yourself an advantage - an extra 70% or so point advantage helps a lot!
Things I've learnt so far - there is better, more comprehensive advice upthread, but this is stuff I've learnt the hard way in the last couple of weeks, and might be handy since it is from a newbie perspective:
1. Scout. If you're going to move a squad somewhere, first send a scout team. If you think that an enemy might attack from a direction, detach a scout team and send them off in that direction as a picket. Everything is so much easier when you know where they are before they engage your main force.
2. Discard any rock-paper-scissors ideas you may have from standard RTS games. Yes a machine gun is effective against infantry, but infantry are also effective against a machine gun crew. Volume of fire is the important thing. If you've located some enemy infantry, don't be satisfied by sicing a machine gun on them, they'll probably suppress the crew before they've got set up. Instead set two machine guns on them, as many squads of infantry as you can, and see if you can call in some mortars.
On a similar theme, anti-tank guns are badly named. They should be called anti-everything guns. But they are very effective against tanks. Never ever move a tank anywhere you haven't first moved infantry.
3. C2 is really really important. Keep platoons together whenever possible. If it isn't possible, keep the HQ near the elements which are most likely to come in contact with the enemy. If you get that wrong, move the HQ asap.
4. It isn't a race. There is something in the wego system that makes me want to rush things. I just have this feeling that every unit should be doing something every turn... This is false. Or rather, sitting in reserve IS doing something; it is fulfilling the very important role of not getting dead, ensuring you have forces ready next turn to avenge what happened on this one.
5. Artillery is a bitch. And doesn't know what side it is on. Keep an eye out for every round falling, and if one falls near your guys forget caution and just leg it.