Tactics (EU2012)

Leap frog your way forward on maps while also rotating through your squad's first move before deciding to perform a second move.
Overwatch, or fire if you encounter something along the way.
This helps you maintain battlefield awareness including map size, squad spacing, and flank openings.

It will also help make sure you have someone with a move left to take action should you encounter aliens.

Save putting your soldiers on overwatch until the end of the turn. This tactic is important for 2 reasons. 1. Aliens get a free move when they are seen and if the alien moves into view of a soldier that has already been put on overwatch they cannot use that turn to fire. You have to rely on them having a reaction shot during the alien's turn. 2. If you want to move them somewhere else you can't because they are locked once on overwatch.

Alternatively, put several secure units (like snipers) into overwatch before revealing enemies. Your soldiers will open fire on aliens as they scramble for cover and the penalty to reaction fire will be more than compensated by the absence of a cover penalty. If you follow this up with careful Run & Gun tactics you can clean up weaker groups before they have a chance to fire at you.

Also, with all the other equipment such as medkits and nano fiber vests and such, the grenade is often overlooked. It is a good idea to have at least one grenade on hand, because a grenade is guaranteed damage, regardless of cover. Better yet, it destroys cover, making a poor shot into an easy shot.

Cover vs Firing

While shooting at enemies is always better than nothing, if you miss or don't kill the target, said shooter is exposed to return fire. Unless you are confident in the shot, or have a second shooter, it may be a good idea to hunker down.

Hunkering down in full cover gives -80 acc to enemy aliens, making it highly likely that nearly all alien shots will miss, or in the worst case scenario, non critical damage. This is especially useful for scouts, as they can mark targets for snipers and live to spot the next turn. Be sure to hunker down as the last move, so the scout spots for all your shooters.