Transaction fees may be included with any transfer of bitcoins from one address to another. At the moment, many transactions are typically processed in a way where no fee is expected at all, but for transactions which draw coins from many bitcoin addresses and therefore have a large data size, a small transaction fee is usually expected.
The transaction fee is processed by and received by the bitcoin miner. When a new bitcoin block is generated with a successful hash, the information for all of the transactions is included with the block and all transaction fees are collected by that user creating the block, who is free to assign those fees to himself.
Transaction fees are voluntary on the part of the person making the bitcoin transaction, as the person attempting to make a transaction can include any fee or none at all in the transaction. On the other hand, nobody mining new bitcoins necessarily needs to accept the transactions and include them in the new block being created. The transaction fee is therefore an incentive on the part of the bitcoin user to make sure that a particular transaction will get included into the next block which is generated.
It is envisioned that over time the cumulative effect of collecting transaction fees will allow somebody creating new blocks to "earn" more bitcoins than will be mined from new bitcoins created by the new block itself. This is also an incentive to keep trying to create new blocks even if the value of the newly created block from the mining activity is zero in the far future.
