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. Early on when accuracy is poor and weapons are weak a grenade is a great way to dispatch Sectoids.

Muton berserkers have a handy habit of chasing down the soldier that shot them. If unprepared, or early on in the game with weak weapons and soldiers, this can be hard to deal with. Later on in the game with stronger characters and weapons it can be used to your advantage. If there are 3 or more soldiers in a line/group use the first soldier on the end to draw the Berserker to the group. Then shoot the berserker with the next closest soldier and repeat along the line. If executed properly the berserker will move from one soldier to the next each time getting closer to the soldier next in line to shoot him. This tactic is especially useful when using the alloy cannon, a weapon with great power but short range. It is also useful if you have a heavy with Bullet Swarm or a sniper with double tap because you can encourage the berserker to move into position instead of your soldier moving and only having 1 shot.

Plan before you commit

Do not use your soldier's turns separately, like, select unit 1, do something, select next unit, do something... First plan the movement and actions of all the soldiers, and only then commit to actually doing it. Instead of taking best shot possible with each soldier, one after another, it might be a good idea to first check which soldier sees which enemy, and has which chance to hit - for example, one of your squad sight snipers could only see one target with 100% CTH on it, and your other squad sight can see that target with 100% CTH on it, and another with 80% CTH on it - while it could seem as a better move to fire on the first target with the second sniper when you select him and look at available targets, doing so will mean you cannot do any reasonable damage with your first sniper this turn. Also, consider what opportunities indirect use of explosives may provide - you may first remove cover of several aliens, then shoot, to maximise your chance to hit, consider how you can move to improve your sight or chance to hit, etc. It is also a good idea to plan for the worst case scenario, having backup plans - for example, leaving Heavy's turn for last, so that he can blow enemies up in case you miss them, or, commit to firing first with your soldiers that are least in danger (snipers, or those behind good cover) so, in case enemies live, you can retreat your soldiers in low cover or in danger of being flanked, instead of having them already spent their turn and locked in a danger zone.

High Cover vs Low Cover

Low Cover not nearly as useful enough as High Cover. While in High Cover you can count on most likely not being hit, and Hunker Down behind it means in most cases that enemy will have 1% chance to hit you, Low Cover means you will most likely be hit than not, and Hunker Down will not save you from being hit as well. Generally, consider using Low Cover only when there is absolutely no way to use High Cover, and always place and advance your soldiers around the map by moving from high cover to high cover. You should never have exchange of shots with aliens with one of your front soldiers being behind Low Cover, except when you have no other choice (like, pinned down in a corner of a map, or all nearby high cover blown by explosives). Having even one unit behind low cover means aliens will focus their fire on that unit and very probably kill or damage it.

Cover vs Firing and Hunker Down

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.

A viable tactic using hunker down is putting snipers in the back (out of enemy LOS) and other units in enemy LOS but behind high cover and in Hunker Down. Enemies will either try to shoot with a very miniscule chance ot hit, relocate (sometimes flanking themselves or making themselves easier targets on subsequent turn) or just go overwatch. This effectively gives your sniper team extra turns to shoot at the aliens (and lower their numbers). However, watch out for enemies with AOE attacks like Thin Men or Mutons, since AI will use it without hesitation in such case.

Also remember that Heavy soldier can go into Hunker Down after he already fired once, if he has the Bullet Swarm perk.

AI "Panic"

If AI unit has no AOE attack, has no enemy in LOS which is exposed/flanked, is himself exposed/flanked, and sees a unit which is on overwatch, it will completely skip its turn. AI seems to run out of options and "panics". Therefore, you can "lock down" units like sectoids and floaters (on the ground), or Mutons if they already used their grenades, or Thin Men if you carry medkits, by simply flanking them with one of your units and putting one of your soldiers that is visible to them on overwatch (can be the flanker, can be different unit).

This can allow you to advance your Arc Thrower carrying soldier, or take free shots on the enemy until it dies, or just save yourself from harm. Using this is way superior to just taking the shot with your flanking unit, because in case you do not kill it, AI will move to cover on its turn and fire back, plus, in a situation when your unit flanks 2 or more enemies, he can only theoretically kill one of them (except using grenades, but then flanking was probably unnessecary), plus flanking does not always guarantee a hit, etc. However, by going overwatch, you can single-handedly keep all flanked enemies at bay while giving yourself freedom to deal with them in whichever way you prefer.

Notice, however, that you must have no units exposed/flanked by an alien locked that way, or alien will fire. Also watch out for aliens with grenades or other AOE attacks.

Do not fear the enemy which is unknown

Enemies can be in two states: activated or not. When you start a map, all aliens are not in activated state, and are bunched up in packs of up to 3. They roam the map (actually, teleport around the map until next teleport will put them inside your LOS, thats when they make a movement animation) or even stay in place until discovered. When spotted on your turn, or coming into your LOS on their turn, a small cutscene will play, and aliens will always make a move, usually into cover. They will never take an offensive action at the turn (yours or theirs) at which you met them. Only once activated, starting from their next turn, aliens start to act as individual units, taking turns in the same manner as player does. (two actions per turn, move/move or move/shoot, overwatch, etc.)

This means that as long as you have no activated aliens on the map, you are completely 100% safe from any kind of harm. You can have every enemy carry a grenade and yet bunch up your soldiers next to each other and never be in danger, as long as those enemies are not active yet. You can be in the open and never be in any danger as long as there are no active enemies on the map. You never have to fear an enemy that is not activated. In a situation when you have no active aliens on the map, you can play a completely different game, and to a big advantage.

While usually you'd try to stay mostly in high cover, spread up if enemy is carrying grenades, doing so when there are no active aliens can actually hurt you, because when they pop on their turn, only one or two of your soldiers will get a chance to react, since others will not yet have LOS on the enemy. Or, aliens may appear from the side of your line formation, meaning it takes you more than one move to get your soldiers into position to fire on spotted aliens. And so on. If you start thinking about situations when there are aliens on the map that are active and when there are not as separate situations, in case there aren't any active aliens it may be optimal not to stay in cover and spread out, but have cover reachable in 1 move, while staying bunched together, thus still being safe in case you cannot take down spotted aliens in one turn, but at the same time giving you benefit of having all your soldiers fire an overwatch shot against spotted aliens. Also, as long as you kill the spotted aliens in the turn you spotted them on (or in the turn that goes after the turn they came into your LOS, if it happened on their turn), you do not have to worry about going into cover, because you will again have no active aliens present on the map.

Also, notice that firing on an alien that you have spotted but that has not spotted you (this can rarely happen when you're behind cover, or easilly happen with battlescanner) will activate the pack, but only if you hit. If you miss, you will not activate them.

Mind Wall

If you are tired of mind controlling aliens after you got Psionics and if you have lucky to have 5/6 Psionic soldiers you can set your psi squad to be permanently in a Telekinetic Field that gives all units (including the aliens) inside +40 Defense. The ability has a 4 turn cooldown so you need 5 soldiers equipped with it to always have 1 unit activating it at the end of your turn. This tactic works ideally on open areas like smaller UFO maps and most abduction and Council missions. Even if the aliens are protected within the field you just need not to set your soldiers on Overwatch so that they'll not fire at the aliens, and if you combine it with Dense Smoke and/or terrain cover you'll get +80 Defense stats. The only vulnerability of the field is to grenades, so take out first any aliens with explosive weapons.