When buisnesses have a "pay with bitcoin" they usually use a third party service that converts bitcoin to dollars for them, but I don't know how that could work for individuals.
I think the easiest for you would be to make a profile (and wallet) at an exchange, get the bitcoins sent there and then convert them to USD and sent to your bank account. I'm not up to speed on what the best ones are, but Coinbase is used by a lot of big buisnesses for the service mentioned above and seems easy to use.
Bitcoin transactions are fairly simple once you get your head around them. Wallets have
adresses and you need to tell him your adress once you have a wallet so he will know where to send the bitcoins. Wallets are mathematical proof (
which is too complicated for me 
) that you own your adress.