1990 Toyota Corolla water pump

Disconnect battery ground cable, then drain coolant.
Remove righthand engine mount.
Remove No. 2 and 3 timing belt covers.
On models equipped with power steering, remove front mount hole cover, remove mount attaching nut and through bolt, then remove mount.
On models equipped with power steering, remove electric cooling fan.
On all models, disconnect water inlet and water bypass hoses from inlet pipe, Fig. 27.
Disconnect heater water hose from inlet pipe.
Remove water inlet pipe attaching nuts and clamp bolts, then remove inlet pipe and O-ring.
Remove dipstick and dipstick guide, plug oil pump body hole.
Remove water pump and water pump pulley. Do not get coolant on timing belt.
Reverse procedure to install.

I would add to great advice by Raz:

Check condition of timing belt and replace if necessary, you will have to remove the motor mount on that side to get it out.

Also check the oil pump seal, if leaking now would be best time to replace it.

Also check lower timing belt cog (on crank), it slides over a woodruff key and if any play it will affect timing. You can buy new ones from Toyota for about $60.