Measure the countertops carefully with a measuring tape. Transfer the measurements to kraft paper and make a pattern. Cut out the pattern and lay it over the countertops, taping corners together to make a perfect match. Mark the locations of the sink and faucets. Roll the pattern up and take it to the countertop fabricator.
Remove everything from the cabinets and under the sink. Turn the water off at the main water line. Also turn off the water line valves under the sink.
Prop a flashlight to light the connections under the sink. Unscrew the water lines from the faucets. Remove the faucet mounting bolts under the sink, using pliers if necessary to loosen the bolts. Gently pry the faucet up from the sink, using a wide putty knife to loosen the plumber's putty. Set the faucets aside.
Look under the countertop. Generally, the sink is screwed in place, although some sinks are glued down. Remove the screws from below. Using a putty knife, work it around the edges of the sink until the plumber's putty or glue is loosened, then gently pry the sink up.
Cut the caulk between the backsplash and the wall with a utility knife. Slide the putty knife along the wall behind the backsplash. Tap with a hammer if necessary to force the putty knife into the space. Use a crowbar to pry the backsplash off the wall, pressing it against the putty knife blade to avoid further damaging the wall.
Look inside the cabinets under the countertop. Most manufacturers use screws or glue to attach the countertop to the base cabinets. Unscrew the countertop or use the putty knife to break the bond between the countertop and cabinet.
Lift the countertop off the cabinets. Recruit a helper; countertops are heavy.
Evaluate the base cabinets before installing a new countertop and determine if the cabinets are salvageable. In many older mobile homes, the original cabinets were a type of pressboard, easily damaged by water. The cabinets may have deteriorated beyond repair.
Repair and paint or stain the old cabinets. Also repair any damage to the wall with spackling paste and repaint before installing the new countertop.
Run a bead of construction glue over the top of the cabinets. Lift the new countertops in place, one by one, and fit them into the space. Once all the countertops are butted tightly together and aligned with the cabinets, screw through the cabinets and into the bottoms of the countertops.
Reinstall the sink and faucets, using plumber's putty or silicone sealant according to the manufacturer's instructions.
Caulk around the edges of the backsplashes, smoothing the joint with a wet fingertip. Allow to dry completely.