Turn off the water to the faucet by shutting the water valves under the sink. Turn the valves all the way to the off position, or clockwise on most pipe valves, to shut them.
Pull out the plug on the front side of the faucet with a pair of pliers and unscrew the set screw under the plug with an Allen wrench. Take off the handle by pulling it up and away from the faucet.
Remove the handle dome -- the round nut under the handle -- by turning it counterclockwise with a pair of pliers or your hands, if possible. Unscrew the cartridge nut right under this part with a wrench.
Remove the cartridge by picking it up and out of the faucet with your hands or a pair of pliers. Replace the cartridge with a new one designed for your 7800 series faucet.
Replace the cartridge nut and tighten it with a wrench to secure the cartridge inside the faucet. Replace the handle dome and tighten it. Then replace the handle and tighten the set screw. Replace the plug by pushing it into the round screw hole.