Depends what you're using to create and broadcast the transaction (txn). If you're using a web/GUI wallet, then there's usually an option somewhere. If you're crafting txns by hand or interested in the protocol, the miner will receive any unspent BTC from the txns (any amount from the input that's not sent to the recipient or back to you as change).
In theory, the lucky and hardworking miner that's solves the block containing your txn will be rewarded handsomely with 25 BTC and the fees from all txns contained in the block. In practice, most miners are in a pool, so the reward will be shared with all miners participating in the same pool as that lucky and hardworking miner