Fixing a leak in your bathtub fixture is something you can do yourself. If you have taken apart lavatory faucets, the bathtub is very similar. However, should anything go wrong, be aware that replacing the tub faucet is more difficult than a lavatory faucet. If you have any doubts contact a licensed plumber.
First, turn the water off to the bathtub. There may be water supply shutoffs at the tub. Look on the backside of the wall where the tub is (if possible) and there may be an access panel to get to the valves. If not, you may have to shut off the water on a branch line or at the meter where your main water supply comes into the house.
Take apart the tub faucet according to the instructions provided with the fixture. If you do not have instructions, take careful notes or make a drawing of how the pieces fit together so that you will be able to rebuild the faucets again.
Once the tub faucet is apart, remove the existing cartridge and take to a hardware store or a plumbing supply house. Be sure to note the brand of tub faucet that you have.
Install the new washers and reassemble the tub faucet fixture.