Been a while since I played it, but best I remember, combat from fallout 1 through tactics were all very similar: turn-based once it started.
I do vaguely remember triggering combat once or twice by clicking on the weapon to fire, instead of waiting for combat to "happen."
edit: Clicking with the other mouse button than the "reload ammo" button. IE, if reload was left-click, I right-clicked, or somesuch.
In general, the combat action button at the bottom of the screen will show your possible attack, once combat begins. Since it's turn based, you wait for your turn to come up, and you'll see a series of green lights over the bar. These are your action points, which give you a certain amount of, well, action each turn.
To attack, click on the weapon icon, which should turn your cursor into a red crosshair. Find a target and click on it.
Eventually all of your green lights will be gone, or most of them (most attacks use more than 1 action point to execute, so you might have a lone leftover AP after some attacks). Click on the "end turn" button. The enemies will go, and then it will cycle back to your turn (if you're still alive!).
Note that you can run out of ammo on a gun. There should be another green bar - this one, vertical - next to the combat picture of the weapon, if it uses ammunition. When the bar is depleted, you're out of ammo. Right-click on the picture of the gun until the text in the box changes to "reload," then left-click it once to reload. Resume killing!