In Genesis and about a year later it seems that there were no transaction fees, only the block reward (50 BTC at that time).
Block 2817 (Feb 3, 2009) was the first one to contain three transactions, two of which paid a fee of 1 BTC. Generally, though, people didn't have to pay anything back in 2009. Blocks were nearly empty, and I think satoshi had set the size limit to 32MB. The next one is
over 10,000 blocks later.
That's a historical thread regarding this matter:
https://bitcointalk.org/index.php?topic=48What made some transaction have fees and others not have fees at that time?
From the link above:
There's a small transaction fee for very large transactions. The node that generates the block that contains the transaction gets the fee.
If the same money gets sent again, it won't incur the fee again. If all you have is generated coins in your wallet, if you send them all in one huge transaction, it has to bundle hundreds of 50 bc coins together. After that it's just one line to send the combined unit.