Replace a car's water pump by draining the coolant, removing any belts attached to the pump, unbolting the pump and installing the new pump. Be sure to properly install the gasket that came with the pump, and monitor the car for leaks upon first start.
If your car's water pump is behind the timing belt, consult a repair manual for additional steps to take.
Make sure the car is completely cold before attempting this job. If your car's radiator has a drain plug, remove it to drain the coolant. If it doesn't have a plug, remove the lower radiator hose. Coolant is highly toxic and sweet-tasting, so be sure to drain it into a sealable container and properly dispose of it.
Take care when installing the water pump gasket, especially if your pump uses a paper gasket. Ensure both of the surfaces are free of any debris, including pieces of the old gasket. Use blue RTV sealant on both sides of the gasket to make a good seal. Make sure you don't move the gasket while installing the pump.
Once the pump is installed, replace the drain plug or lower hose, fill the radiator with fresh coolant, and start the car with the radiator cap off. Top off the radiator as the air bubbles circulate out, and carefully watch for any leaks. Continue to check for leaks for a few days after the repair.