How do Japanese keyboards work?

So uh, I know about English keyboards... 26 letters in the alphabet, pretty simple. But what about Japanese keyboards? I was just reminded because of the Quick Look for The Typing of the Dead. Doesn't the Japanese written language have about 50,000 characters? How the hell do you fit 50,000 characters onto a keyboard? It would need over 50,000 keys, right? That seems unfeasible.