Tips and Hints
For each soldier, decide to specialize in light or heavy weapons. Heavy weapons are generally better, but have higher skill requirements; for best results, don't buy anything past the Advanced Combat Gun (requires 1 point of Light Weapon skill) for anyone destined to use heavy weapons. You'll want at least half of your soldiers to train for heavy.
Soldiers start at level 0. A soldier gains 1 skill point for every level gained, which he or she can do a maximum of 12 times. A soldier can receive at most three commendations, which provide one additional skill point each. Some soldiers start with "free" skills, and implants found in equipment crates don't subtract from your skill point pool, so it's possible for a soldier to have more than 15 points worth of skills. It takes 12 experience points to go up a level, so experience maxes out at 144 points.
The skills required to use advanced weapons and equipment often mean that other equipment becomes "skill free". For example, any soldier with a Servo System can wear Standard Armor and carry Light Stimulants and a Small Medic Kit without spending additional skill points. Keep an eye out for such opportunities.
Units have hit points and "fighting strength" (the yellow number next to the cardiac line). If a soldier's fighting strength gets too low, he or she will panic, which means they have only 1 AP and are unable to attack. Some attacks that do no damage (i.e. didn't penetrate the armor) will still reduce fighting strength, so units cannot "tank" and be combat-effective indefinitely. The stat recovers naturally at one unit per turn, or three per turn if the soldier rests. Maximum fighting strength is equal to the soldier's level or 3, whichever is greater.
Moving horizontally or vertically costs one AP per square. Moving diagonally costs two APs per square. This is geometrically incorrect, but does mean that moving from point A to point B has the same cost regardless of the route chosen (cf. "taxicab geometry" or "Manhattan distance"). The only exception to this rule is Jet Pack jumps, which compute distances correctly.
Weapon heat is reduced at the start of your turn. If your weapon shows "hot", you won't be able to fire defensively. Hot weapons can be fired, but with a chance of jamming up for a few turns (or even exploding).
Once you have met the goals, the mission ends when you end your turn. The Scay'Ger don't get a parting shot.
When defending against melee attacks, note that moving diagonally costs two AP, but attacking diagonally costs one. This can be crucial when kiting hard-hitting melee units like the Gore'Ther, which can hit you if you are a "knight's move" away.
You can open doors and crates diagonally. When breaching a room, it can be useful to "charge up" APs by having the soldier in front of the door sleep for a turn, and then having a diagonally-adjacent soldier open the door.
The order of operations for spawn points during the enemy turn seems to be: (1) new spawn appear, which can attack; (2) flamethrower flames burn out; (3) more spawn appear, which can not attack. If you use a flamethrower to prep a spawn point for destruction with explosives, you can rely on not being spawn-killed, but can't rely on the field being clear when the flames die. (The spawn-and-attack action is a significant issue in the Wilderness Campaign.)
Enemy units won't move if they don't have a path to you. Closing doors and blocking passages with the flamethrower will cause enemy units to freeze in place. Bear in mind that melee units can attack diagonally, even if they can't move through the adjacent squares, so standing inside a corner formed by two obstacles can draw enemies to you.
The Enhanced Laser Gun can capture enemy units that have 3 or fewer hit points. There's no way to tell how many HP an enemy unit has, but if the target isn't weak enough, you won't be allowed to fire in mode B. The laser's mode B shot does 0-2 points of damage, which makes it difficult to capture Ray'Ther, and difficult or impossible to capture Dec'Ther. Captured units can move immediately, stay captured for the duration of the mission, and can perform most actions that soldiers can, including resting, pushing boxes, and opening equipment crates. They get an extra AP if they are near a Banner, can be healed by your units, and do not panic, making them excellent "tank" units. Gore'Coo can use defense mode, where their unlimited ammo and non-heating weapons make them vastly superior to human forces. Captured units have their maximum HP capped at 15.
In the campaigns, try to open all of the equipment crates. The base campaign is fairly generous with the equipment points, so if you can't open a few of them you won't be in trouble, but some of the crates contain implants that upgrade your skills. In the expansion campaign, equipment points are tighter, and some crates hold equipment you can't get elsewhere (e.g. crowbars).
When you buy a new weapon, you get a full refund for your old weapon, so feel free to swap weapons around to match the mission. The purchase happens before the refund, so you must have enough equipment points in the bank to buy the weapon you want, even if it's less expensive than the weapon you're giving up. Note you do not get a refund for old armor.
If you can't hear speech in the cut scenes and briefings, turn up the music volume.
During the enemy turn, you can hold down the right mouse button to "fast forward" through the animations. This can save time if you've screwed up and know you will need to reload.