My 1990 Buick Park Ave Electra AC blower fan will not shut off,I had to unplug it so it would not run down battery,can someone help and let me now how and what it is?

I'd say check the relay.

can you tell me where the relay is located at?

Not sure but on your model year , I think they moved the relays to under the dash on the pass. side?

On mine it's uner a plastic covering on the firewall, the wider rectangular one, s;b labeled C4##...

is the relay a tin looking square thing or black? I'm a girl dont know much about cars but I'm learning,Thank you for your time and help ! Debbie

It could be "tin" in appearence if it's already been replaced. There s/b 2 black square relays, then this one right next to them, again more rectangular. Is it under the hood? If so, just follow the wiring from the fan back to it.

Check out thread #166- 94 PA Blower wont shut off.
I had the same problem with my 1991 Buick PA. Turned out to be the Blower Control Module. I bought one at a junkyard for $40. (The dealer wanted $150). That was the problem. If you are looking for a replacement and you look at the module you will see an AC Delco #16061602, however, that part is no longer made. The replacement AC Delco part is #12484912.
If you have a PA with dual climate control (passenger side control) you may not have a relay. You have a Blower Control Module which is difficult to get to. It is on the top of the housing that houses the fan. You must remove the relay center and push aside the fuel line to get to it. Unplug two connectors and remove 3 scews to remove it. If you have single climate control then you should have a blower control relay under the hood (again just above the blower housing). These relays are black and square on my car.

The blower motor is bad. I know it sounds strange but the same thing happened to me and I replaced the motor to fix it. It is an easy fix.