The first step you must do is shut the water valves off under the sink that supplies the hot and cold water to your faucet. Once you shut the water off under the sink you must disconnect the supply line that feeds the water to your faucet, on the new models there is usually a threaded connection at the supply line and the faucet it self and in this case you only have to remove the connection at the faucet and replace the faucet itself. To remove the faucet itself there are nuts that hold the hot and cold water handles in place, use a wrench to remove the nuts (if they are in a hard to reach area and you can't get a typical wrench in there you may have to purchase a basin wrench from your local hardware store, see picture below)
To make it easier for you, I recommend removing the existing faucet and bringing it with you when you purchase the new faucet to make sure that the hot and cold water pipes on the old faucet match with the new one you will purchase. Some of the faucets have a different distance between the hot and cold water pipes.
On some of the older models you will have a direct connection to the faucet and a threaded connection at the water supply; in this case you will remove the connection at the water supply and have to buy supply lines that are long enough to go from the water supply to your new faucet. I recommend using the stainless steel supply lines they come in sizes from 12" and up (see picture below).
Once you purchased all the needed materials all you have to do is connect the supply lines to your water supply valve and install the faucet the same way you uninstalled it and connect the supply line to your faucet and you have completed the task of replacing your bathroom sink faucet. Keep me posted with any questions and good luck with your project.