Arright.
Chaotic, the rundown is this.
Every unit has a "Move" stat, represented as little green bars on its icon (the big squares don't count). Each turn, you can move or jump as much as this move stat allows. Moving and jumping in any direction costs 1 move, except on diagonals where it costs 1.4 move (so moving diagonally twice can be rounded up to 3 move). If you jump or step off a high point, you must jump down so that you end the move on the ground, or no higher than 0.5 off the ground, else your unit will be destroyed.
Every unit has "Range" and "Ranged power", as bright and dim yellow bars on the icon. You can shoot once during each unit's move. A range table in the first post can help you see how far you can shoot. A shot cannot travel over obstacles or units (units count as 1-high obstacles), and the line drawn between the center of the attacker and the center of the target must not intersect too much height difference. I'll make a table for this one later. You also can't shoot a directly adjacent unit. (at range 1, diagonal shooting is fine)
Every unit has "Melee power", as orange bars on the icon. You can melee attack once during each unit's move. Melee attacking over a diagonal takes up 1 move, because the units aren't really adjacent then.
Every unit has "Shield power", as skyblue bars on the icon. This affects the combat rolls.
When attacking, the attacker and defender both have a die rolled. Attacker adds his power to the roll (ranged or melee), and the defender adds his shield. If the attacker's result is equal or more than the defender's, the attack hits and a die is rolled for the location of the hit. Refer to the hit table in the first post for hit locations.
...I think that's pretty much it. In a nutshell, Pandar is right about everything.
I'll make a table for shot angles and range.