Plan your turns before doing anything. Don't move your soldiers in the order the computer gives you. Always have your soldiers act in the most advantageous order possible. Got a Heavy? Have him shoot first, to activate Holo-Targeting for the rest of the squad (or blow up the enemy's cover with a rocket). Got an Assault? Save him for last, Assaults are very mobile and can deliver the coup de grace when and where you need it. And so forth.
Plan your teams and abilities ahead of time. If you have two Supports, one should be a field medic with Extra Heals + Extra Moves, the other should have Suppression + Extra Reaction Shot to make him a nightmare for enemies trying to move. Then you pair the suppression guy with an Assault who's got Flush.
Have rookies throw grenades. They can't hit very well with firearms, but grenades are guaranteed damage.
Always have at least one low-rank soldier on your team. Train replacements.
Understand that you WILL lose soldiers, especially at higher difficulty. Feel free to get attached to them anyway. I know I did.
Don't bother with smoke grenades. I lost several guys before I figured out smoke does not provide any benefit (despite what the ability claims).
Don't bunch up. Enemies can and will grenade your ass.
Don't ever, ever, EVER hang a dude out in the middle of the field with no cover when you've got active aliens. No matter how necessary it seems, just don't. You WILL lose any uncovered soldier the aliens can see.
Do your moves in two stages, i.e. don't have a soldier do a double move. Have him do a single move, then another single move. Sometimes you'll spot aliens on the first move, allowing you to change your second move.
Skip lasers, go to plasma.
The early game is about satellites. Launch early, launch often.
Get to squad size six. 50% more muscle on the field = win.
