When your engine is on, the water pump circulates coolant, or antifreeze, in the cylinder head and the engine block to cool the engine down. After the coolant passes through the engine it's sent back into the radiator to be cooled before entering the engine again.
Parts you'll need:
REMEMBER: If your water pump uses "O" rings instead of gaskets, do not use silicone. Just remember to clean up ALL the surfaces that the rings will seal against. You don't want any leaks when you're finished!
Let the RTV silicone cure for about 10 minutes, then install the water pump and gaskets so they're situated exactly the same as the parts you removed earlier.
Before installing the water pump bolts, use a thread sealant or medium strength Loc-Tite (blue) on the bolts to make sure there are no leaks or bolts loosening later on.
Install the water pump bolts, and torque using proper torque technique and specifications for your application
Always use the right torque settings when installing anything with a gasket. If you over tighten (this is easy to do), you can wreck the gasket before you even start the car. If it's not tight enough, you'll get leaks.
Reinstall any brackets and hoses you removed, and always use new hose clamps.
Reinstall or retighten anything you removed or loosened when you removed the water pump (ie. plastic panels, fans, shrouds, etc.)
Close the radiator drain and fill the cooling system.
Reinstall the radiator cap and start the engine.
Check for any leaks and you're done.