Your soldiers operate on the principle of line-of-sight. If they can’t see the enemy, then they can’t fire at them. Be careful when moving into uncharted areas as you could get a nasty shock.
Your melee-based warriors can make short work of enemies, but they need to get in close. Keep them covered with ranged attacks.
The dots under each warrior show how many action points they have left. Keep an eye on these when trying to move and shoot in the same turn.