Probably the easiest and user friendly for a beginner are some of the various systems and I would have to say the Spyderco Sharpmaker is one of the best. Now a bench stone, oil or water stone is probably one of the cheapest but, flats stones take a bit more time to learn to use properly and if you don't know what your doing you can ruin the edge pretty bad and then will need to fix it with a grinder. Belt sanders and grinders and so on are one of the fastest ways to do it but those again take a bit of skill to use right without messing your blade up. Files and sandpaper can also be pretty good but take longer. Just some heads up stuff to educate you about some of what people are talking about in this thread, strops are used to debur and help get a finer edge on the blade, you can actually use some news paper or cardboard or a piece of leather or denim to debur the edge as well, by doing a scraping motion with about a 20 degree angle on the edge. Another tool is a steel, if someone has mentioned this and I missed it sorry, its used to straighten the edge of a blade out for a kind of quick fix but doesn't really sharpen the blade. There are some ceramic sharpening rods that can be used but free handing with a rod is probably one of the hardest methods in my opinion, trying to keep a consisted angle on the blade can be difficult and takes practice.
My personal favorite is a oil or wet stone and is one of the best ways in my opinion but that is just my preference.
Hope some of this can help you out and get you on your way to putting a razor sharp edge yo your blades.
Also I would recommend taking a look on youtube there are some decent vids that can help you get a better idea on some of the sharpening techniques, the best would be to find someone you know that can show you in person but if not the videos should do.
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