I've played off and on for a few months. Generally, I take on a massive project (like a castle), work on it for a while, get bored, stop playing for weeks and then come back to try something new. Pretty addictive in that sense, but I wish building were a bit faster.
To your question, you want to look for the file on your computer with the game data. I'm running Vista, so the extension is C:\Users\My Name\AppData\Roaming.minecraft, look up the corresponding folder if you're running another OS. You'll see a folder in there titled Saves with separate folders for each world. Copy the folder you want and paste it into the saves folder of your other computer.
Disclaimer I've never tried it, but it should work.