Faucets and Fixtures:

How to install bathroom faucet
Clean the surface where the new faucet will sit and insert the rubber gasket between the faucet's base plate and the sink top to create a watertight seal. If no gasket is provided, seal the perimeter of the faucet base with plumber's putty, and then insert the tailpieces through the holes in the sink top. If your faucet has water-supply tubes already attached to the tailpieces, as shown, feed them through the middle sink hole and press the faucet into position on the sink. From the underside, thread a washer and mounting nut onto each tailpiece, then tighten the nuts firmly with a wrench.
Virtually all bathroom faucets come with a pop-up mechanism that allows you to open and close the drain by pulling up on a lift rod behind the spout. Remove the stopper from the tailpiece, and then install the tailpiece as shown so the pop-up port faces the spout.