You want to click on the crosshairs box right next to the weapon, I think its blue - If you're hovering the cursor over the right thing you should have a tooltip pop up that says "primary fire mode." Click on that, then you'll get a menu with firing options, different ways to shoot with the weapon. Click on the box with the type of shooting you want, then you'll get a red line from the soldier to whatever you want to shoot, and finally left-click to end that red line on the alien, bad guy, whatever, and it should fire.
Sorry I don't have a screenshot handy...
Edit: Depending on what version you're playing, you should also have a tutorial slideshow you can access from the main menu, look at "Tactical Mission."
