Once you pick out your new faucet fixture, you must get your old one out of the way. This is fairly simple to do. Begin by shutting off the water to the faucet you are going to replace. If you cannot find the water shutoff for that sink alone, you can also shut off the water to your entire house. This could be a bit of an inconvenience, but replacing the faucet should not take you too long so just make sure no one else desperately needs to use the water during that time.
After the water is shut off, turn on the faucet to let any excess water drain out of it and then plug up the drain so that you do not lose any pieces or parts down it while you are working. Next, disconnect the water lines that feed the faucet so that you are free to remove the old one. You will also have to figure out how your faucet is attached to the counter itself.
Your old faucet may be attached on the bottom of the counter or the top. Either way, you can get it off easily enough, but you will have to know which side to approach it from. Once you have unscrewed your old fixture, simply pull it off the sink and put it aside. Make sure that you thoroughly clean the area where the old fixture was attached as well. Remove any grout, putty or other substance that may have collected around the old fixture over the years.
When that is done, you are ready to install your new sink faucet. Simply fit it into place, attach it to the counter and connect the water lines. Be sure all connections are secure and turn the water back on to test your handiwork. If you need help with any of your bathroom plumbing, you can always call your local plumber.