I've done this job, only because the mechanic at the time wouldn't take the 32 hours away from other customers to do it. It's a bitch. Recommend you do a general search in the forum for the same topic - I've seen a couple threads with a lot of good info and even some step by steps.
In short, the easiest way to get at the heater core is to take out the front seats, and everything (yes, everything) from the dash, except for the dash itself. The radio, the wood, the instrument cluster, glove box, speedo cable, etc etc.
If you're going to do the job, I'd recommend having an assistant who will take careful notes of what came from where and how it goes back. Some stuff will be obvious.
I recommend you inspect and replace as necessary the heater control levers. The parts are available from a couple vendors that are still in business. Also, if you're replacing the core, I'd consider replacing the blower motor as well (unless you can say with certainty that the thing is good).
In lieu of replacing the core with a new one, I'd recommend taking it to a radiator shop and having them repair the coils as necessary. A complete radiator rebuild will cost about $250, but a heater core would be much less, and thus more cost effective than buying a new replacement.
This job isn't "un-dooable," but it does take patience and time. It definately wasn't a weekend job for me