1. Gather necessary tools and parts: new water pump, gasket, coolant, adjustable wrench, socket set, screwdriver, pliers, and a bucket.
2. Allow the engine to cool down if it's been running.
3. Locate the water pump: It is usually found on the front of the engine, near the bottom.
4. Place a bucket under the car to catch any coolant that may leak out during the process.
5. Disconnect the battery: This is a safety precaution to avoid any electrical issues while working on the water pump.
6. Remove the serpentine belt: Loosen the tensioner pulley and slip the belt off the water pump pulley.
7. Remove the hoses: Disconnect the upper and lower radiator hoses from the water pump. If necessary, use pliers to remove any hose clamps.
8. Remove the bolts holding the water pump: Use a wrench or socket set to loosen and remove the bolts securing the water pump to the engine block.
9. Remove the old water pump: Carefully pry the old water pump off the engine, taking care not to drop it. Clean the mating surface on the engine block to remove any old gasket material.
10. Install the new water pump gasket: Place the new gasket on the mating surface of the engine block, ensuring it is properly aligned.
11. Install the new water pump: Carefully position the new water pump onto the engine block and align the mounting holes. Hand-tighten the bolts to hold the water pump in place.
12. Tighten the water pump bolts: Use a wrench or socket set to tighten the water pump bolts in a crisscross pattern to ensure even pressure. Tighten the bolts to the specified torque as per your vehicle's repair manual.
13. Reattach the hoses: Reconnect the upper and lower radiator hoses to the water pump. Secure them with hose clamps.
14. Reinstall the serpentine belt: Place the serpentine belt back onto the water pump pulley and adjust the tensioner pulley to tighten it.
15. Refill the coolant: Add coolant to the radiator until it reaches the "Full" mark.
16. Reconnect the battery: Reconnect the negative battery terminal to the battery.
17. Start the engine: Start the engine and let it run for a few minutes to circulate the coolant. Check for any leaks around the water pump and hoses.
18. Test drive: Take the car for a short test drive to ensure proper functioning of the new water pump and cooling system.
Note: These steps are a general guide, and some variations may exist depending on the specific model and year of your 1991 Buick Regal. It is always recommended to refer to your vehicle's repair manual or consult a professional mechanic if you are unsure about any step.