as a beginner, you should DEFINITELY take a course in proper safety and rigging when doing any sort of climbing.  AND you should go to your nearest outdoor store/book store and buy some books.  there are plenty out there and if you ask somone in the climbing section of an outdoor store, i'm sure that they'll point you toward a good book for TR (top-rope) rigging.

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that being said, it's good that you're asking these questions before you go out and try it on your own, but unfortunately, it's a very broad question that even the best answer would take a long time to write (hence the books).  furthermore, rigging really depends on the situation (i.e. are there bolts? are they good? are there trees? are there good boulders to sling? what type of equipment do you have available?). the answers to these questions will help you narrow your inquiry for the case at hand.

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for natural anchor rigging, i'm a big fan of using static line set up for a USSR (Ultimate SlingShot Rig, aka "a russian").  the problem is that it requires a knowledge of knots and their applications.

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if there are bolts around, either a simple sliding-x with limiter knots or a quad rig will do the trick just fine.

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if you have webbing and natural anchors, then there's a vast number of combinations you could use.

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brad makes a good point, in that you need to familiarize yourself with knots, various rigging methods, and their approriate applications before you try to interpret a particular and unique situation on any given route/area.

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if all these terms sound like greek to you, then i HIGHLY suggest going and investing in books and classes, or find and EXPERIENCED and knowledgeable climbing partner to show you the ropes, so-to-speak.  i apologize if our answers seem dismissive, but the fact is: it's thorough and complete knowledge that keeps you safe (and this can't really be found on a forum - forums are more for clarity for particular issues and throwing ideas and conversations around).  please do some reading of possibilities and come back with questions that narrow your query down to the demands of your route.  there are plenty of good people on this site, who are happy to help out with clarifying questions, but it's a lot to ask of someone to give you all the possibilities for TR rigging on a forum (no offense intended).

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good luck, learn well, climb well, be safe