Turn off the water underneath the faucet by shutting the valves on the water pipes.
Find the small screw head on the side of the faucet base. It is underneath a cap on some models. Pull this cap out and unscrew the screw with an Allen wrench. Remove the screw completely and set it in a place where it will not get lost.
Grasp the neck of the faucet around the curved portion for more leverage. Place your other hand on the base itself just below where the faucet neck meets the base. Pull up to remove the faucet neck from the base. It will click out of place, since it snaps into the base during installation.
Remove the base if necessary by unscrewing the locking nuts underneath the faucet below the sink's counter top with a basin wrench and lifting the faucet up and off the sink.