GURPS Lite is available for free, and includes the basic rules on how to do things, combat, etc. It doesn't include the introductory "What is a GM?" stuff to save space; though that does show up in the Basic Set. You can extrapolate quite a lot from just what's in Lite - a lot of the stuff in even the Basic Set that's not in Lite is corner cases (how far can I jump? What can I shift or drag, instead of lifting?), clarifications (how long does it take me to dig a hole?)... and lots more skills and abilities!

Mook has some very basic combat examples worked through here

In a little different vein, Feral Sword Wielding Wizard has some fight scenes from movies he's gone through and labeled with GURPS combat maneuvers, so you can see how they work! (Just keep in mind this is with a bunch of optional rules!)