Shop Rat: "Hello, Bob's Bike Shop. How may I help you?"
Customer: "Well. I have a flat tire. And I have these....funny....tubes"
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Presta VS. Schrader 101
We'll stick with these two since these are what you most often see in the U.S.
Schrader:

Looks like your car's valve stem. Can be filled with any compressor or at the gas station.
Presta:

To fill a presta valve, unscrew the top nut (righty-tighty, lefty loosey) and depress. The tube is ready to be inflated. Most modern bicycle pumps have either "smart heads" capable of inflating either valve stem style or two holes in the pump head (the smaller hole fits the presta valve).
If you have a compressor, an old-school pump or you need to top off at the gas station invest ~$1-2 in a valve stem adapter:

A note about those little plastic valve caps: You don't really need them. Most racers toss them (extra time/extra weight) but if you really really ~must~ have those little plastic gems, just ask. We have plenty.

