First a quick survey, then click through for a great how-to video on knife sharpening.
You'll need a sharpening stone (or bench stone) for sharpening and a sharpening steel (or rod) for honing. For stones, I like one with a diamond edge, but it's not necessary for sharpening success and non-diamond stones will only set you back less than $10. For the steel, they are usually included in knife sets, or pick one up for less than $20 at most cook's supplies.
Here's Marc Bauer of the French Culinary Institute demonstrating the method I learned (as a student at FCI, although not from Chef Marc.)
After you watch the video, read Emma's step-by-step post on how to sharpen your knives.
A note on frequency: Professionals sharpen their knives a lot more often than home cooks. I cook at home often, probably using my chef's knife at least four times a week, so that is a knife I sharpen on a stone about four times/year. I hone it on the steel almost every time. Once you work with a properly sharpened knife, you'll know when it needs to be sharpened again. Honing re-aligns the blade whereas sharpening on a stone actually scrapes off a little of it, so obviously you want to hone more often than sharpen.inexpensive sharpening steel (AbleKitchen.com, $6.74) and Smith's Diamond Sharpening Stone (Amazon, $24.86) or this budget-friendly 12-inch sharpening stone (Restaurant Source, $2.89)
Related: Feeling lazy? Get Your Knives Sharpened By Mail