I have a slightly older style bathroom sink faucet, the style that you pull the knob up to turn on and adjust left or right for hot and cold. When I push it back down to shut the water off, it makes a clunking sound. Any ideas why and how to fix it? Thanks for the help..

It sounds like a moen château, or a price pfister. Simply replacing the cartridge should fix it.
1-800-pfaucet for price pfister. Moen customer service at 1-800-555-1212 for 1-800 411

I have a different take on your problem. Sounds like water hammer to me. If it's water hammer charging the cartridge won't help. If your house is under 40 years of age then you have air chambers installed. "Water hammer" happens when you abruptly shut off the water. You have at least 40 pounds of pressure pushing the water flow. The weight of the water hitting a 90 degree bend causes the sound that you hear. We put in air chambers to cushion the hammer much like the shocks on your car.
Back in the 60's we were required to to put air chambers on all bath lavatories and kitchen sinks. Over time water and condensate built up in them and they must be recharged. First turn off the house at the main house shut off valve. Then open hot and cold faucets at the farthest bathroom to prevent air lock.(This is important.) You will find under each fixture little brass or chrome valves. These are called angle stops. With a small pail held under the angle stop to catch the run off look under the handle of the stop and you will see a nut with the stem running through it. This is called the bonnet packing nut. Put your wrench on it and back it off counterclockwise. Now open the stop and remove the stem and washer assembly, The stop will began to drain. When it has quit draining reassemble the stop and move on to the next one. Do this on each one of your angle stops. There will be six of them in a two bath home. When you are done, close off the faucets you have opened, turn on the water to the house, and give yourself a pat on the back.
You have just recharged your air chambers and saved yourself a hefty service call bill. Hope this helps you out TOM