Where is Water Pump located on Toyota Corolla?

The water pump is usually located on the front of the engine and driven by one of the accessory drive belts, that circulates the coolant by causing it to move from the lower radiator-outlet section into the engine by centrifugal action of a finned impeller on the pump shaft.

To replace water pump,the timing belt has to be removed.
If you notice car overheats and also makes loud sound/noise.Then yes water pump has to be inspected.
If the bearings in the waterpump were failing, it could be loud.The water pump is mounted behind the timing belt. The Timing belt has to be removed before the water pump.However,to conform if water pump is faulty or not. You can grab the waterpump pulley and wiggle it. If it has any play, it is bad, if it does not, then it is not your problem.

In that case Thermostat can be the cause of overheating.If you need details for thermostat replacement,check the link below :---

http://technoanswers.blogspot.com/2011/12/thermostat-replacement-on-toyota.html

But if water pump pulley is making noise when you wiggle and it has play,then water pump is the cause of problem.See the water pump location diagram below.This will give you better idea of where to look for water pump on your Toyota corolla.

There is one more procedure,where you dont have to remove timing belt to remove water pump,but that procedure is very conjested and with very less room.You cannot remove water pump very freely.
In that You actually  slip the pump out without actually removing the timing belt, but the engine mount and timing covers have to be removed.

This basic details will help.Thanks.

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If you need dis-assembly or replacement instructions for any other auto/car part, or you want to ask question related to your car/truck jeep problem then please leave the comment with your details, so I can provide you the required instructions and solutions.

Also see this for more help:----

Water pump replacing procedure for all vehicles?

http://technoanswers.blogspot.com/2011/11/water-pump-replacing-procedure-for-all.html

How to Replace a Water Pump

http://schematicsdiagram.blogspot.com/2011/07/how-to-replace-water-pump.html

How to route Water Pump Belt for 1992 Oldsmobile Cutlass Ciera?

http://carbeltrouting.blogspot.com/2011/12/how-to-route-water-pump-belt-for-1992.html

How to replace Water Pump on Acura Car models?

http://repairhelpcenter.blogspot.com/2011/11/how-to-replace-water-pump-on-acura-car.html

How to Remove Water Pump on Toyota Previa?

http://technoanswers.blogspot.com/2011/12/how-to-remove-water-pump-on-toyota.html