A bathroom sink typically has three holes. The faucet usually comes with a pop-up stopper assembly.
Bathroom work space can be cramped. If you have a pedestal sink, check to see whether the bowl is securely attached to a wall bracket. If so, you may be able to remove the pedestal. If you have a sink with a cabinet below, it may be easier to detach the trap, remove the sink, and set the sink aside to install the faucet.
If there are no stop valves under the sink, install them before putting in the new sink.
Whether you reuse the old supply tubes or buy new ones, make sure they are long enough to reach the stop valves. Purchase fittings (either 3/8- or 1/2- inch) that will fit your stop valves.
About 2 hours to install a bathroom faucet with a pop-up drain stopper assembly
Screwdriver, adjustable wrench, putty knife, groove-joint pliers, basin wrench
Shutting off water, working under a sink, attaching plumbing parts
Shut off the water, remove the drain trap if needed
New faucet, new pop-up drain (usually comes with the faucet), plumber's putty, supply tubes if needed
Shut off the water and turn the faucet on until water stops flowing. Disconnect the supply tubes and the mounting nuts. Loosen the setscrew that holds the clevis strap to the lifter rod, pinch the spring clip, and slide the clevis strap off the pivot rod. Pull out the old faucet and clean the sink deck.