How does the bitcoin transaction fee get paid to miner(s)?
The very first transaction in every block is called a coinbase transaction. This coinbase transaction is created by the miner themselves, to pay them the block reward and the fees from the transactions in that block. At the time of writing, the block reward is 12.5 BTC, and then the total of all the fees is added to that, and the coinbase transaction is created to pay themselves that total.