Randy
First thing to do is drain coolant to a lower level so that when you remove the core, it isn't full. If the core is the original and the heater box has never been out, I suggest that you pull the box. Remove hoses from the firewall side, and air tube for motor.
The control cables can be marked with tape to ensure correct location upon re-assembly. The electric connectors come off with ease.
Remove any screws connecting the duct work to the heater box.
Remove nuts from engine side of firewall and the unit is ready to remove from car to bench.
The housing can be taken apart and the core accessed. This is a good time to do a cleaning of the inside of the box, and check/replace any foam that is missing or deteriorated. (kit is available from
www.detroitmuscletechnologies.com) Its amazing how much dirt, dust etc can be inside after all these years.
This is for non-A/C heater box.
Im not sure if A/C units can be pulled apart this way, most likely the heaterbox can be split by removing the screws around the perimeter. Cables and wiring to be removed first. The one half should just pull away , without disturbing the cooling coil. The coolant hoses would be the only connections to remove on the engine side.
Hope that helped a bit