How do you replace the coolant reservoir? - 2003 Buick Park Avenue

Clips in and out. Make sure the engine is cold and unclip hose from bottle on top and bottom. Coolant will come spilling out, but thats okay. Replace the coolant reservoir and then re-attach the hoses, fill the coolant reservoir back up until the F line. Also top off the radiator just in case. Start the engine, let it run and drive it 5-10 miles. Then go home, let the car sit and cool down for an hour, and then re-check the coolant level in the reservoir. If low, fill back up to the F line. Then you're done!

Check the water pump and see if coolant is around it.

Drain the reservoir, & clamp coolant lines. Remove coolant lines to reservoir. Depending on location, generally it involves 2 to 3 screws that hold it on the vehicle frame. Remove & replace.

So the level keeps dropping in the reservoir? If you have to keep adding coolant to the reservoir, the system is leaking or losing coolant somewhere. Have the system pressure tested to find the leak. Is the reservoir itself leaking? When the level gets low enough, first the reservoir will go dry, then the radiator level will start to drop.
Here's how the reservoir works: coolant is under pressure from the radiator cap seal. As coolant heats up from hot engine, it expands, and pressure forces the radiator cap seal up, coolant is forced into the reservoir-remember the hot mark on the reservoir? When car is shut off, coolant contracts, creating a vacuum in top of radiator. This vacuum works to suction coolant back from reservoir into the radiator, keeping the radiator topped up, and coolant should now be at the lower cold mark on the reservoir. It is a closed, sealed system. The only loss of coolant will be a very small amount of evaporation from the reservoir. If coolant level keeps dropping, there is a leak somewhere.

You should only have to replace coolant overflow reservoir if coolant is leaking from reservoir. Sensor should be sold separately.

WAIT UNTIL YOUR ENGINE IS COLD,YOUR RADIATOR PRESSURE CAP IS LOCATED ON THE COOLANT OVER FLOW RESERVOIR, THATS WHERE YOU ADD COOLANT WHEN COOLANT LOW,YOU POUR COOLANT IN THE OVER FLOW RESERVOIR UNTIL COOLANT LEVEL REMAIN AT FULL COLD MARK DONT OVER FILL OVER FLOW RESERVOIR, WHEN COOLANT LEVEL STOP DROPPING WHEN ADDING COOLANT AND COOLANT LEVEL STAY AT COLD MARK ON THE RESERVOIR YOU RADIATOR HAS THE CORRECT COOLANT LEVEL IF COOLANT LEVEL KEEP DROPPING CHECK FOR COOLANT LEAKS AROUND RADIATOR AND THE TOP AND BOTTOM RADIATOR HOSES, LOOK FOR COOLANT LEAK AT WATER PUMP GASKET OR SEAL OR LEAK AT WATER PUMP WEEP HOLE IF YES REPLACE WATER PUMP.

The black rubber hose may be bad and needs replaced. This hose should connect to the radiator at the radiator cap and run along the firewall to the coolant reservoir. Also the coolant reservoir might be cracked and leaking on to the rubber hose, if this is the cause just replace the coolant reservoir which may be a dealer only item, check at you local auto parts store and they will tell you if it is a dealer only item. If you have to replace the coolant reservoir, make sure the car has not been run and the coolant at the radiator is cool, cause when the engine is hot the hot coolant runs into the coolant reservoir till it cools and returns to the radiator when engine is turned off and cools.

It probably got overfilled at some point. There's a max line on the reservoir that you shouldn't fill it over. Coolant expands as it heats up so if there's too much in the system, it's normal for it to overflow.

that is so easy unhooked connector plug,unhook hose,loosen three bolts take off coolant reservoir.
New sensor comes with reservoir

Your description may actually be your answer, so to speak. You mention 'generally as engine is cooling or if coolant is added too quickly'. It sounds to me like the reservoir is over-filled.
When the engine is cooling, coolant tends to flow back to the reservoir (plastic 'jug' where you add coolant). A bad radiator cap or one that was replaced with too low a PSI rating can easily allow too much to fill the reservoir and and occasionally overflow it. Most reservoirs use a rubber tube to drain excess coolant so it may appear to 'leak' near the front left wheel or left side of engine.
Replace your radiator cap. (did they pressure test the cap too?)
Make sure you check your owner's manual for the proper PSI. My sources show 15-16psi, but that sounds a little high to me. Also, make sure you have the correct (50/50) anti-freeze/water mixture.
After you replace the cap, make sure the reservoir has the right amount of coolant and isn't over-filled. (To 'fill cold' line) Drive the engine until hot, then park the truck and see if the problem is fixed. Good Luck!