Shaven legs are one of the cannons of bicycle racers everywhere. There is a very simple technical reason for this practice: shaving your legs makes it that much easier to clean a wound, if you are so unfortunate as to fall off of your bicycle. Really, that's all. (Well, shaven legs do look better, but that's relatively unimportant. They certainly are more aerodynamic.)

The practice of shaving legs was imprinted on American popular culture in the 1979 film "Breaking Away":

Cyril: Hey! Are you really gonna shave your legs?
Dave: Certo! All the Italians do it.
Mike: Ah. Some country. The women don't shave theirs.

Mom: What's the matter?
Dad: He's shavin'.
Mom: Well... so what?
Dad: ...his legs.

If you want to shave your own legs, here's how:
1. Find a hair clipper, and remove excess hair growth. You can't get to this with a regular razor, there is too much.
2. Using shaving gel and the best 3+ blade razor you can find, wet your legs (perhaps after a shower), apply shaving gel, and shave in long, continuous strokes.
3. Repeat step 2 about once every three days.

You only "need" to shave the portion of your legs that sticks out of your bicycle shorts. Be careful around the pereneum.