Someone answered one of my questions and I would like to give him reputation. How do I do that? Does the computer do that itself? This is my second day using this site, so I can't quite navigate this site.
You click on the hollow "V" icon to the left of the answer.
voting up (up arrow) answers you like or accepting their answer both increases their reputation.
It is important to accept an answer when you think it answers your question pretty well. If it not but it's very helpful anyways you can just vote it up and leave the question open.
It is not really a matter of rewarding people, but rewarding good questions and good answers.
See this question for reference: Why is OP unable to upvote any answers?
You first need to Register your account: click on the Log In link in the top menu on every page, and choose how you prefer to register, e.g. using existing
gmail account, giving your email address and more options.
Once you have permanent and registered account on the site you can give (and get) reputation like all others have said already.
As long as you're not registered member, you can't do many things that are related to reputation.
The main way to give others rep, as mentioned in the other answers, it to upvote the other user's posts (10 points for answer upvote, 5 for question), and accept an answer (which gives the person who posted that answer 15 reputation points).
You go to the post in question and approve their answer.