I just did mine in my 69' with a/c, should be the the relatively same process.
drain coolant, remove hoses into the core on the firewall, metal plate(s), and the rubber grommet that secure the in and out pipes. Also disconnect A/C lines if applicable.
remove upper dash pad and lower dash, vacuum lines,(mark them!), and cables that operate blend door puller thingy's
you are now staring at a black heater box
on my 69' there is an upper mounting bolt that runs from the heater box the dash pad mounting area, above where the glove box would be, remove this
move back to the firewall area and remove the nut(s) that are holding the heater box to the firewall. On mine there were 2. One was located in the upper left corner of the firewall, kind of near the hood spring, and the other was on the lower right area of the firewall kinda near the auto trans dipstick.
Remove these, mine were 7/16".
Once these are out, the heater box will be freed up and easily pulled out from the passenger side seat.
Once the box is out, remove all the side clips, pop apart like a clam shell, replace core and reuse rubber bumpers if not too far gone, reseal clam shell, reinstall heater box.
If you do not have AC, your heater box is probably alot smaller than mine, so the firewall bolts that pass through may be in different locations. My firewall bolts were fitted with very large flat washers, then with a chinsy kind of stamped metal "speed nut", that pops off with only a few twists.
Hope this helps!
J