A friend owes me some money and we agreed to settle that debt in bitcoins. How can he transfer some bitcoins to my account, without me having to pay him for it?
You only have to do a simple transaction. You have to create an address (for example, this one (which is mine): 1CnCc2Dp35BZboHE8AZvoyrQXCFFaHUvTZ) and tell him to transfer Bitcoins to that address.
You dont have to pay anything for the transaction, but your friend need to pay the transaction fee.
You and your friend need to agree on the bitcoin-to-fiat exchange rate, and assuming he/she is already in possession of the required amount of bitcoins, he can just send those bitcoins directly to your bitcoin wallet.
If you don't yet have a bitcoin wallet you can just download one, like multibit (https://multibit.org/), create a receiving address and give it to your friend so he can send the bitcoins to you.
Once you receive the transaction, and after 3 or 4 confirmations from the bitcoin network, you can assume the debt is settled.