When replacing an old faucet there are generally three things to consider: how many holes your sink has, how far apart they are, and whether or not you will need to replace the drain.
Most bathroom sinks usually come with three different hole configurations. The most popular configuration is two holes four inches apart on center with a center hole between them (three holes total). Another similar configuration is two holes eight inches apart on center with a center hole between them (often called a spread set configuration). Finally, there might be just a single hole, which is a common configuration for newer sinks and faucets.
You will need to purchase a faucet that matches your particular hole pattern. It is not recommended that you try drilling holes in your sink or try to make a spread set fit in a 4 inch configuration. One exception to this rule, however, can be made for some single hole faucets that are designed with a wide base that will cover the extra holes in a 4-inch configuration.
Usually, it is a good idea to replace the drain when replacing the faucet. Typically, bathroom faucets are sold with pop-up drains but you can also get them with just a plug. If you do replace the drain, consider buying a new trap and tailpiece as well. It is much easier to work with new pipes than old and the cost is not prohibitive. For detailed step-by-step instructions on how to complete this DIY project, watch this friendly how-to!