All those choices look intimidating?
Than this page is for you!
The first thing to know is that GURPS is a toolkit and lets a GM build any setting in any genre they way. That requires a lot of overhead for the game system to provide everyone with anything they want. However for any given game you only need a fraction of the available material (Skip magic if your playing SciFi, Skip guns if playing typical fantasy, etc) and you as the player need even less than the GM. The core rules are in this free 32 page PDF called GURPS Lite (available in multiple languages) and even they include stuff you wont need for every game.
Mooks site has a page on What is Roleplaying that may be useful a well.
Also look at this... Mooks Game Geekery GURPS Grab and Go
GURPS has only 4 primary attributes DX, HT, IQ and ST with some secondary ones like Move and HP based off those. A skill is based off one of those attributes but may use another in specific situations. For example Gins (pistol) is DX based to shoot someone, but your GM may ask you to roll against IQ instead to recognize a specific model or figure out something about your gun.
To succeed at a task you roll below your effective skill on 3d6. Shooting someone may take penalties because of range or darkness but get bonuses from a good sight, proper bracing or even taking your time. You the player do not need to remember these mods, that is the GMs job. Just ask what your mods are to evaluate your chances.
Points spent on a skill represent training and experience at it. Most skills default to another skill or an attribute. This allows you to at least try something without any training, though your not as likely to do well as if you had training. Anyone can Jump or run for example but a trained athlete knows how to be better at it. Any modern person can drive a car but if you have training and experience your better able to handle tough situations like ice on the roads or avoid accidents because you have learned what to watch for.
There are a LOT of skills in GURPS because it is designed to work in any setting. However only some of the skills will be available in any specific game and only some important to you, based on what you want to do. There is an offical free PDF that lists skills by category. It is a great help in choosing which ones you want. Also some games use templates which are kind of like charecter classes and have a short list to pick from.
Combat can be fairly simple or complex depending on what the group wants.
Basically you roll to attack using your weapon skill (including unarmed combat skills) and your opponent rolls to defend and if you succeed and they fail you hit. Then roll damage and subtract thier DR (Damage Resistance) from any armor they have.
Each Turn (about 1 second long) you choose a maneuver ( I recommend Combat cards to remember them for your first few games) which boils down to Move, Attack, Defend, or Prepare (Concentrate and Ready) or some combination of those. Not all games will bother with the full range of options but they make for more intereting tactical choices
The same with Hit Locations or bleeding rules, not every game will use them but if you want them they are available. There are many special swtiches or options a GM may allow but as aplayer you dont really need to worry about all that, just waht the Gm wants to use. For example he may use Mook rules that make it easy to take out minor foes like ninja hordes or stormtrooper marksmanship.
The point is all the options add flavor and choices but increase what you may need to remember so are OPTIONAL and not required.