Mark a 2-foot square box on the floor in the lowest-lying corner of the basement floor. Tear up the concrete inside this square with a jackhammer, beginning at the spray-painted lines and working toward the foundation walls. Wear safety goggles, gloves and ear protection when using the jackhammer. Use a hammer and chisel when you get close to the wall to prevent damaging the walls with the jackhammer. Remove the broken chunks of concrete from the corner.
Dig a hole for the sump pit liner in the soil where you removed the concrete, placing it at least 8 inches away from the walls to protect the foundation footers. The hole must be as deep as the liner, and at least 6 inches wider. The liner is a plastic container with holes that allows water to flow into the sump pit.
Place the liner into the hole, centering it, and fill the gap around the outer edge of the liner with gravel. The gravel prevents most of the dirt from entering the sump pit, while allowing water to flow into it for drainage.
Place plywood boards against the walls in the corner if the floor is a floating slab. If there is a gap between the floor and the walls, it is a floating slab. If there is no gap, skip this step.
Pour gravel onto the soil around the hole, using enough gravel to go about an inch above the bottom edge of the concrete slab.
Mix concrete, following the instructions on the packaging, and pour it onto the gravel around the sump hole. Smooth the surface of the concrete with a trowel, and allow it to set for two days.
Connect a male PVC adapter to the discharge port of the sump pump by screwing it into place.
Measure the depth of the sump pit liner, and cut a piece of schedule-40 PVC pipe with a hacksaw that is slightly longer. Glue the pipe to the PVC adapter with PVC cement. Attach the electrical cord for the sump pump to the PVC pipe with plastic electrical ties.
Insert the sump pump into the sump pit, placing it so that the float can move unobstructed inside the pit. The float is the round rubber ball on the side of the sump pump that rises and falls with the water level inside the sump pit. The rising and falling motion of the float activates and deactivates the pump's motor. Cover the sump pit with the lid to prevent objects from falling inside the sump pit.
Attach a check valve to the PVC pipe that extends from the pump, using a hose clamp. The check valve prevents water from flowing back into the sump pit, protecting the pump's motor from burning out from overuse.
Cut a PVC pipe to fit between the ceiling and the top of the check valve. Connect it to the check valve with a hose clamp.
Drill a pilot hole through the header joist with a quarter-inch drill bit. The header joist is the wood beam on top of the concrete wall. Go outside and locate the pilot hole. Drill a 2-inch hole through the header joist with a hole saw, centering it over the pilot hole. Return to the basement when you are done.
Insert a piece of PVC pipe through the hole in the header joist to the outside. Glue a 90-degree PVC elbow to the end of the pipe inside the basement. Point the elbow straight down, and place it against the PVC pipe that runs from the pump to the ceiling.
Make a mark on the pipe where it will reach into the PVC elbow, and cut the pipe at that height. Glue the end of the pipe to the open end of the PVC elbow.
Mark the PVC pipe outside the house about a half inch where it extends past the header joist, and cut the pipe at that mark.
Glue a 90-degree PVC elbow to the pipe where it extends past the header joist, pointing the elbow straight down.
Dig a trench in the ground from the PVC elbow to the location where you want to drain the water. The trench should be slightly wider and deeper than the PVC pipe.
Apply a thick bead of caulk around the PVC pipe on both sides of the header joist to seal the joint.
Place a 90-degree PVC elbow into the ground directly underneath the one that extends from the header joist. Cut a section of pipe to fit between the two elbows, and glue the elbows and pipe together.
Place PVC pipe inside the trench from the elbow to the end of the trench, and backfill the trench.
Plug the sump pump into a ground-fault circuit interrupter (GFCI) outlet. A GFCI outlet has a circuit breaker built into it that kills the circuit in the event of an electrical short, such as one caused by water seeping into the line.
Vacuum the basement floor and wash it with a mild cleanser.
Draw the path of the electrical cable for the in-floor heating system onto the floor. Keep the cable at least 3 feet away from the sump pump to reduce the chances of the cable shorting out due to exposure to water.
Lay cable strapping onto the floor every 2 1/2 feet along the path you drew for the cable. Attach the strapping onto the concrete floor with construction adhesive.
Lay the cable onto the floor, following the path that you laid out. Attach the cable to the straps as you reach them.
Connect the cold lead conductors (the wires that lead from the cable) to an ohmmeter to test the cable for damage. The ohmmeter should provide a reading between 10 and 250 ohms; if it doesn't, replace the cable.
Mix cement-based mortar, following the manufacturer's instructions. Spread the mortar onto the floor with a trowel, adding enough mortar to conceal the cable. Allow it to set for the time specified by the manufacturer.
Add a second coat of mortar to the floor with the trowel, and allow it to set for the specified time.
Install the surface for the finished floor. Tile is an ideal choice in this instance as it is resistant to water damage, easy to clean and allows the radiant heat from the cable to seep through, heating the floor and the room.
Hire an electrician to connect the heating cable system to the thermostat and main electrical box. Most municipalities forbid unlicensed homeowners from wiring circuits into the main box due to safety issues.