//No idea how to play this.
A good source of information is to observe how this game played out:
http://www.bay12forums.com/smf/index.php?topic=150207.0That page is the start of all this. It contains information on character sheets, how combat works, etc. In general, though, the most important things to remember are that your movement range (7.5) is your half, or
blue, movement range. This indicates how far you can move in a single turn and still be able to shoot, go into Overwatch
(get a shot on enemies that move within 10 tiles, which is also your total firing range), etc. Multiply your movement/mobility by 2 and you get your full, or
yellow, movement range; this is your Dash distance. Since your mobility is 7.5, you could run up to 15 tiles in a single turn, but you can't take any other actions if you move any more than 7 tiles in one turn.
The rocks and trees you see on the map are cover. Always keep that between you and the enemy, obviously.
Blue lines indicate heavy cover that confers 45 defense
(a 45% lower chance for enemies to hit you), and usually reduces damage by 1.
Green lines are partial/half cover, and only confer 30 defense
(30% lower chance to get hit), and a 66% chance to block 1 point of damage. Cover is drawn in a straight line, and an attack will incur cover penalties if it crosses that line. However, if your attack does not cross that line
(for example, if you flanked an enemy behind a wall by leaning around said wall for a shot), the enemy does not get a cover bonus. Also, being closer to your target can greatly increase your chances to hit them.
Word of warning:
AP grenades WILL NOT hit an enemy if a cover line lies between them and the site of the explosion. Always make sure you're tossing AP grenades against exposed enemies, or throw them behind the cover, otherwise they will do nothing. HE grenades will, however, hit enemies behind cover, and have a good chance to explode said cover entirely and leave aliens woefully exposed to follow-up shots.
Those are some basics. I really do recommend that you check out the link above, though, as you can find pretty much everything pertinent about how to play the game from that starting point.