Well, without really turning this into a spoiler, I'll list my basic infantry strategy:
80% shooting
20% moving
I try and keep my forces pretty spread out and in cover (as for JasonC's mission, note there's more terrain cover there than you think... damages and all), advancing when I know I'm going to get shot at. Splitting one squad and going for a "pincer" type movement on a known target has a good effect... I usually lose 3-5 guys but the target can't shoot everyone at once, and while the 80% is firing the 20% can come around the flank and do its duty.
To be honest I have just started playing missions that are in fairly open terrain... I played CMBO and CMBB and I couldn't stand open missions due to the difficulty of getting infantry across the map. But using a proper recon force (half squads!) and really shooting the hell out of a target once it pops up, I can usually make pretty good advances.
Another tip: Think about what works and doesn't work when you are on the DEFENSE, and capitalize on D's weaknesses when you are on the offense. This sounds silly, but it improved my game a lot once I did this.
Hope that helps.