How do you remove and install the heater core in a 1981 Chevy Surburban?

There should be a plastic housing just outside the firewall on the passenger side of the vehicle, and a corresponding housing unit in the vehicle under the dash. You will need to remove the housing from the inside of the vehicle to access the heater core. The housing is usually held in by a few bolts that go through the firewall. (On my 89 they are "rivets" so to speak, and have to be unbolted from the engine bay.) Once the housing is out the heater core should be removed relatively easy. There was one bolt in particular that was up under the unit that was difficult to get to, but I found with the correct socket and a angle driver I could use a long extension in between the wheel well and the housing to get the bolt loosened with a socket wrench. Other things to remember are to removed the hoses from the heater core before you try and pull the barb fittings through the firewall, and the unit has coolant in it so be prepared to soak that up. (It took me 3 days to figure out just how to get to the heater core and roughly 3 hours to put it back together. The core can be bypassed so that the truck remains functional during the removal, but if you're not a patient person or don't have the time to dedicate to the project it would be far easier to just pay someone else to replace it.)