3. Unscrew the Old Faucet
Use a basin wrench or a pipe wrench to loosen the nuts holding the supply lines to the old faucet. If they are stubborn you may need to squirt some penetrating oil (like WD-40), onto the nuts and wait a few minutes for the oil to work it's way into the threads. Use the wrench to turn the nuts counterclockwise and pull the lines away from the faucet. You then use the wrench to unscrew the mounting nuts from the bottom of the old faucet. If there's a lift rod for the drain plug, that needs to come off too—usually by compressing the spring loaded fastener on the rod.
At this point the old faucet should lift right off unless caulk is holding it in place. If it's stuck to the top of the counter, use a knife to cut away the old caulk and lift the faucet off. Clean off any extra caulk or residue that's underneath the old faucet using a putty knife or a razor knife.
4. Put on the New Faucet
If the new faucet comes with a gasket, lay that down first and then put on the new faucet making sure the holes line up. Re-tighten the mounting nuts using your wrench by turning them clockwise. Reattach the supply lines the same way and then reattach the drain plug rod.
If your new faucet did not come with a gasket, you might want to put a bead of caulk around the new faucet where it meets the countertop. Use a caulking gun to squeeze out a thin line of caulk as you trace your way around the faucet. Wet your finger and use it to smooth out any problem areas.