Replacing a sink faucet is fairly easy. Start by turning off the water at the supplies under the sink. Open the hot and cold taps on the faucet to relieve the pressure. Use a cup to collect the water from the supply lines as you disconnect them. If you are replacing the water supply lines too, then disconnect them from the supply valves. Otherwise, disconnect the supply lines from the faucet beneath the sink. If you have enough room to work, you can use slip joint pliers, but a basin wrench may make the job a lot easier.
With the basin wrench remove the mounting nuts that secure the faucet body to the sink. If they will not loosen, spray them with penetrating oil and give the oil a chance to work.
If replacing a bathroom sink, disconnect the drain lift rod from the drain pop-up assembly. The two most common styles require loosening a thumbscrew or squeezing a metal tension band to release the lift rod.
You should now be able to remove the faucet body, although the old putty may have a hold on it. If so, carefully run a putty knife around and under the faucet to break the bond. Lift off the old faucet and clean the surface of the sink before mounting the new faucet.