An electric water pump is an above-ground pump that draws the water from your well into your home. This is different than a submersible water pump which is located outside, deep inside your well. An electric water pump is almost always by the pressure tank, or cold water tank. If the pump freezes with water inside of it the housing can crack. When this happens water will spew forth from the pump. This can be fixed by replacing the housing for far less than you'd pay to replace the pump.
Turn off all of the water to your home by turning the shut-off valves to the right until they will no longer turn. Do this as soon as you realize your water pump needs to be repaired, when you see it is leaking. Unplug the damaged water pump so there is absolutely no electricity running to it as you are taking it apart. Prepare yourself with plenty of old towels as there will be water that is still inside of the pump that will leak out.
Lay down a couple of towels under the pump and keep a few more on hand to prevent water leakage from damaging your flooring. Remove the clamp that secures the water pipe to the end of the pump. Take the pump off, and set it on a towel on the floor. Use a wrench to remove the four bolts that hold the casing of the water pump together, then set the outer shell of the pump aside.
Use a wrench to remove the 4 bolts on the outside of the water pump. Set the bolts aside, then pull the outer casing off the pump. Remove the pump housing by squeezing the small clips that hold it in place to release them. Inspect the housing closely to make sure it is cracked before you purchase a new one. Locate the make and model number on the pump. Take the information to a home improvement store. Ask for a housing for that make and model, and get replacement seals.
Replace the damaged housing with the new one, taking out the old seals and replacing them as well. Place the shell of the pump back onto the pump, insert the four bolts and tighten them well, but not too tightly, or you may strip the bolts.
Hold the pump in place, and insert the end of the pump back into the water pipe, making sure to wrap the pipe with Teflon tape first. Replace the water hose clamp and tighten it to secure the connection.
Turn the water to your home back on. Plug in the water pump, and watch it closely to ensure there is no longer a leak.