To attack with a weapon skill, point the mouse cursor at an enemy and press the corresponding button displayed under the skill on the skill bar. (From left to right: Left mouse button, Right mouse button, 1 and 2 on the keyboard.)
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Your combat capabilities are mainly determined by your equipped weapon. One-handed weapons grant two weapon skills each, two-handed weapons provide four. 

You can see what skills you have available on the skill bar at the bottom of the screen. Hover the mouse cursor over the skill icons to see a description of what each skill does.

Melee weapons allow you to attack enemies at very close range. They are quite deadly but you are exposed to enemy fire while you close in for the attack. Try putting tall objects like columns between you and the enemies during the approach.