Rule ONE: Follow orders. If you can't get anything else right, just do that. Go to your waypoints. Build what is dropped. Don't go wandering off looking for something to bite you. Those squads the comm put you in? Yeah, that means you're supposed to STAY with those people!
Advanced marine skills: (Note, ONLY for those who have completely mastered rule ONE) Think on your feet. Team's only got two RTs up and you're passing a smoking node? Request an RT. You just happened to glance into a hive room and there's a hive building? Scream for a PG. Good comms are always ready to alter their strats to take advantage of good luck. But don't think TOO hard. If the comm says 'I don't want that RT, get to the waypoint,' you GO! The comm is the man with the ultimate plan, he sees a lot more than you do from the field. Always always always remember rule ONE. It takes precedence over everything.
Sundry other details: Aim at alien, pull trigger. Following rule ONE and moving in groups makes this ridiculously easy, so that even people who can't hit the broadside of an onos can rack up kills when they're combining their lead with the lead of their comrades.
Ask for what you need. The comm can't ALWAYS be watching your health. (the good ones will be, though) And the comm does not ever know your ammo count. If you need it, AND you're in a place that's worth having you in, call for it. Don't beg for meds when you're ten feet from base, please...
Try to always be ready to move on. Get your ammo when you have a second, reload when aliens aren't in the room at the moment. Weld constantly if you have a welder. Lots of great pushes lose all forward momentum because everyone suddenly needs to ammo up, weld up, they want a tfac, they want a shotgun, they need to go to the little marine's room, etc. Just GO. Every second you're humpling the sweet sweet armory is a second the aliens are expanding their territory, their res, and their evolutions.