How do you replace a 1999 Mazda miata water pump?

To replace the water pump on a 1999 Mazda Miata, start by disconnecting the negative battery terminal and draining the coolant. Remove the timing belt cover and the timing belt, then detach the water pump by unbolting it from the engine block. Clean the mounting surface, install the new water pump with a new gasket, reassemble the timing belt, and finally refill the coolant and reconnect the battery. Ensure you check for leaks after running the engine.