Whenever you make a transaction in bitcoin, you point to the previous balance you have from a previous transaction, then you say how much you are sending to what address.

The "fee" is the difference between the amounts.

So if I have 1 Bitcoin, and I send .9 to you, the fee is .1

If you want to make sure you keep some Bitcoin, you just send it to yourself.

So 1 have one, and I send .1 to you, and .8 back to me, the fee is .1

Then when a miner mines a block, any unspent money is now theirs, and they claim it via the address they liked for.