Really its pretty simple. I thought it was gonna be harder than it was but it only took my an hour to have the dash out and another 30 min to get the heater box out. And that was by myself with out looking at the tsrm. If you just follow the tsrm tho itll give you the steps to get the dash out(its called safety pad in the tsrm) start here
http://www.cygnusx1.net/Supra/Library/TSRM/MK3/manual.aspx?Section=BO&P=50 Should be noted tho that the tsrm does not say how to get the heater box its self out. I removed the charcoal canister, undid the ac lines and removed the heater hoses that go into the firewall from the engine bay side. One behind the intake mani and the other behind the exhaust side valve cover. BE VERY CAREFUL NOT TO DAMAGE THESE COPPER PIPES, ONE IS DISCONTINUED AND THE OTHER IS WELL ON ITS WAY TO BEING THERE TOO. Looking back on it I could have done it without undoing the ac but I wanted to pull the whole box and refoam it.(Post 37
http://www.supramania.com/forums/showthread.php?101797-88-7MGTE-White-Pearl-Targa-Lots-of-Pics/page4 ) Remove the dash support bar before trying to pull the climate box. There are a couple 10mm/Screw bolts that hold the ac evaporator side and the same for the heater box side. If i can remember right the evap bolts were black and the heater box bolts were goldish. You have to undo the evap side first and slide it out and to the right as much as possible, then you can undo the heater box and slide it out. once you have it a few inches out you should be able to reach the heater core. Its in the center up under the windshield. Dont forget to replace the o rings for the heater pipes, a few bucks at toyota for piece of mind.
Some pointers that i found made it easier:
Remove drivers seat and drop the column instead of pulling the steering wheel. Seat is four bolts and the harness connector under the back and one bolt at the seat belt track on the trans tunnel. Move the seat all the way forward before unplugging it. column is 2 17mms. There is a spring on the left side of the column for the tilt release..remember how and where it goes. Unbolt the ebrake handle at the trans tunnel and lay it over after you get the center console out, its one 19mm nut and one 19mm bolt(might be 17mms actually). Put the trans in Low or 4th which ever you have and cover it with a hand towel or rag to protect from scratching. Same with steering wheel.
Pretty much all the screws you pull out will be the same so remembering exactly what ones went where isnt too important, only special ones are the ones holding the climate control and the stereo i think. but any 10mm or 12mm bolts you pull try and remember or put in ziplock bags with writing as to where they go.
Dont pull the dash assy straight out. Pull up then out to unclip it.
This thread has alot of pointers and imput.
http://www.supramania.com/forums/showthread.php?92688-Dash-Removal-Writeup&highlight=heater+core
Use the search function and just browse through threads, I did searches for things like "heater core" and "dash removal"
And if you have any more problems or questions just pm me, im on here daily. Good luck!