This article will cover the replacement of a water pump on a 1996 miata. This is generally done when the timing belt is being replaced. You should start off by following this link to a Timing Belt replacement. Then come back to this article to finish. It is always recommended to replace the water pump when the timing belt is replaced as it saves alot of labor. If you do not need to replace the timing belt you can use the plastic tie strap method which will make things go much faster. This picture shows the water pump pulley located in the center of the picture. The four bolts will need to be removed and the pulley taken off. The thermostat housing bolts (arrows) will not need to be removed.
A water pump circulates water from the engine and through the radiator to keep the engine cool. Most cars need a water pump somewhere around 120,000+ miles. Some cars like Hondas have the pump by the timing belt and some are driven off of it. These type of cars should replace the water pump at the same time the timing belt is replaced. The water pump is easy to replace in comparison to the timing belt. If not replaced, the water pump tends to die soon after replacement of the new, tighter timing belt. Many newer front wheel drive cars have the water pump on the left side of the engine. The pump is driven off an accessory belt that will need to be removed first. The belt tensioner will first have to be loosened. Many times the alternator acts as the tensioning device.