Vanitygen gives you an address as well as the corresponding private key in WIF format (starting with a 5, K, or L). In order to import it into Bitcoin-Qt, go into the Console (Help, Debug Window, Console) and type in importprivkey where is that private key you got. It'll take a couple minutes (seriously, it could take a while) while it goes through the blockchain to see if that address ever received any coins, and then it should be a part of the wallet and show up in your list of address on the Receiving tab.

To get a "firstbits" address (which I'm assuming is what you mean by "short"), send some coins to it, wait for several confirmations, and then look them up on a site like blockchain.info. I'm not aware of a tool that finds the firstbits by looking at one's local blockchain, though there probably is one out there somewhere.