My 1991 Buick Regal (3.1 engine) use to start a high RPMs and then slowly, as the engine warms up, the RPMs would come down to about 800, which is the normal. However a few weeks ago, it started to start a higher-than normal RPMs, and instead of coming down as the engine warms up, it keeps going up to a certian point. Then it would stay high, no matter how long I wait for the engine to warm up.

Replace the crankshaft sensor and the cam sensor. I had the same problem. Good luck.

Your battery could be weak, Do you still have the original battery? You can get a new one at basically any auto parts store.

i think you might be right it sounds like your engine is getting over fed fuel you are probably not getting very good fuel mileage either the 3.8 and 5.0 would defintely require the same volume of fuel it is probably playing havoc on the pressure regulators i would get another fuel pump and start there

sounds like your alternator could be givin up slowly, have a charging test done and after a full charge on the battery have it tested as well.

check the hose for the pvc vavle it could be split

egr valve is not opening up when the engine reaches it normal operating temperture

orfis in the accumulator may be clogged.
don't fill with feon bottle upside down(liquid), it will damage the comp.
check high pressure, don't ever exceed 250 psi

Sounds like your car is overheating. If you have a temp gauge it should show that. If you just have an idiot light, by the time it comes on it's already too hot to operate. AFTER the car is cooled down, open the radiator cap to see how much coolant has been lost. Chances are there is alot missing. Add WATER (no sense in adding coolant if it's going to leak out) and idle the car at home. Look underneath as it warms up to find where the leak is.

Take car for trouble code at Autozone or similar store for free. it is probably the idle position sensor.(IPS)

the problem may be a buildup of carbon or fuel varnish deposits in the idle speed control valve (also called the idle air control valve or IAC valve). The cure for this condition is to clean the valve with some aerosol throttle cleaner or engine top cleaner. disconnect the air ductwork from the throttle body. Start the car and run at about 1500 rpms spray the cleaner directly into the throat of the throttle body. Turn off the engine and let sit for a few minutes. Then repeat the process a cpouple of times. if that does not work, you can remove the IAC and clen it by spraying into the two holes on the underside of the valve.If not, then you need to replace the valve.