I generated a paper wallet at Bitaddress and sent my bit coin to it. It says I can check it's balance by going to the block chain and entering the new address.
When I do that I get "first bits not found." So how does one go about checking to see if the bit coin is there?
Are you sure you're entering the full (33-34 characters, starts with '1') address at blockchain.info?
Thank you, that be it.
One more question: Bitaddress generated my private keys, but do I not need to invent a password as well or is my private keys my password?
Private keys are all you need to spend the coins. You can create encrypted private keys as well if you want added protection. See this post for an overview:
Avoid brain wallets though. Personally I would recommend install electrum or armory on an offline PC rather than using bitaddress to generate private keys of any sort.