Summarize the following:
Look underneath your sink for the pipes that run up. Along those pipes somewhere will be handles that you can turn to shut off the water to your sink. Twist clockwise to shut off. Use a sink plug if you have one or a rag.  Nothing will ruin your day faster than having a screw or a washer go down the drain. A compression faucet has two screw handles, one for hot and one for cold, and is the easiest to recognize by sight. The other three types of faucet all have one central, swiveling arm that you can swing from hot to cold as desired. You may have to take your faucet apart before you know which is which, because the internal mechanisms at the base of their arms are all different:  A ball faucet contains a ball bearing. A cartridge faucet contains a cartridge. The materials of the cartridge will vary, but handle often has a decorative cap. A ceramic-disk faucet contains a ceramic cylinder.

Summary:
Turn off the water to your faucet. Plug the drain. Determine what type of faucet you have.