I need to locate the heater core on my Moms 1992 sunbird and I also need tips on how to go about replacing it

May be the easiest heater core i have ever replaced.Disconnect the two hoses going into firewall on the passenger side.Locate a small cover just underneath the glove box .Should be about 10 x 3 inches and have 8 screws i think.It is on the bottom of heater box.remove the screws and cover and pull out the heater core.You are now half way.reverse procedure and you are done.Good Luck!

You should get a Haynes manual. You have to go on the inside of the vehicle and remove the panels, to get to the heater core. Then you have to jack the vehicle up to remove the heater core from the hoses. This is a tedious job and takes time. But not to difficult. I'm not a mechanic, and it took me about 4 hours.

Does the car have A/C? I've seen where the A/C evaporator coil springs a leak and it will be soaked with refrigerant oil, then every speck of dust or dirt that comes along sticks to it. Pretty soon it's plugged solid, the air for the heater has to pass through the A/C coil along with the heater core. No A/C, it could be that heater core fins are plugged. Also, some cars have a "cabin filter" if that's plugged it won't allow air to enter the system at all. Call a dealer or auto parts store to see if vehicle is equipped with a cabin filter. Good Luck!

Yes, they typicaly about the same size as a pen. Make sure that it is just water comming out, and not coolant. If water, this is normall from condinsation, if coolant, you will need to change the heater core.

You will need to pull the dash assembly away from the firewall slightly and remove duct work from heater case on right (passenger)side then the heater core cover,the 2 bands that secure heater core,drain cooling system,remove the 2hoses,and swop out old heater core.

REMOVE OR DISCONNECT

1. Negative battery cable and drain cooling system.
2. Raise vehicle and remove drain tube from heater case.
3. Heater hoses from heater core and lower vehicle.
4. Right and left sound insulators and steering column opening filler.
5. Floor air outlet duct and heater core cover.
6. Heater core mounting clamps and remove heater core.

INSTALL OR CONNECT

1. Heater core and heater core mounting clamps.
2. Heater core cover and floor air outlet duct.
3. Right and left sound insulators and steering column opening filler.
4. Raise vehicle and connect heater hoses to heater core.
5. Drain tube to heater case and lower vehicle.
6. Negative battery cable and fill cooling system.
7. Check for leaks.

Remove all plastic duct under dash bord till you find core

It appears I was incorrect about removing the dash assembly, here are the instructions from a Buick owners club.

Under the passenger dash is an access panel that will allow you to remove the heater core, it really isn't that hard, there are lots of little dash screws and panel screws to remove before you get where you need to be but at least it is roomy. The AC evaporator is located by the heater core. I will give you a tip. I changed mine last year and the heater core that I ordered for my 92 Roadmaster was not correct, when I took my old one out and matched it in a book at the local part store, the heater core for my vehicle was listed as a 96 Caprice???? The car has been in my family since it was purchased new and the heater core had never been changed!!!! Explain that one!Oh yeah, one more tip, if your heater core is leaking, this access panel lowers towards you, if there is nasty sweet smelling water in there it will pour all over you, be careful! Caprice parts are the same as a Roadmaster,so if you ever need anything just look up caprices

The heater core is located there just under the dash in the plastic enclosure. AC parts may also be there. Remove the heater enclosure to expose the core. You will have to disconnect the heater hoses from the engine to remove the core and enclosure. Then inspect the core for the leak, usually at a line connection.
The core can then be soldered or sent to a radiator shop for repair. You should have some expertise in repair to attempt this job on your own, otherwise take it to the shop. Some people would try radiator stop leak since the heater core is part of your cooling system, but I wouldn't recommend it. Remember to replace the anti freeze when you are done.

Aside from disconnecting your heater hoses, the only fix is to replace the "heater core". The "heat" function of your climate control system relies on heated engine coolant to work. The small elbow that you describe, is most likely the condensate drain. The "heater core" and the "evaporator core(for the a/c)", are located beneath the dash assembly in an enclosed housing. The "heater core" should be serviceable without removing the complete housing as with some vehicles. I hope this helps