Unscrew the spout/spout elbow assembly from the front of your countertop unit.
Insert the 1/4" pipe nipple in its place. Screw it flush to the housing, so that the o ring touches the housing, but don't over tighten.
Remove the base from the new filter housing and screw it onto the empty end of the spout elbow. Screw it into the “In” port of the housing. (With most housings, “In” and “Out” can be determined by looking at an arrow on the bottom side of the base.) Again, do not over tighten.
Screw the spout/spout elbow assembly into the “Out” port of the new housing.
Load the new cartridge into the new housing (it's easiest if you invert the unit), tighten firmly, and reinstall the unit on the countertop.