There are many faucets on the market. The single most common mistake is not taking the faucet or the part to be replaced with you when buying the new parts. Before working on any faucet turn the water off and open the lines to drain into the sink. Cover the sink with a towel or cloth to protect it from tools that may be dropped and to prevent the small parts from going into the drain. Wrap the jaws of wrenches with tape to protect the finish of the faucet.
Faucets usually leak because of old gaskets or o-rings and corroded valve seats. The accompanying diagram shows the most common way to get the gaskets and valve seats.