Remove the passenger seat and remove this bolt.

You can actually do a lot of other things first, but you can't avoid removing the bolt and the silly heater duct.
Remove center console.
Remove glove box.
Remove right side speaker grill.
Remove the glove box crossbar.
Remove the 2 piece black plastic heater duct that joins above the glove box - one screw for each.
Remove the white plastic duct behind the glove box (four bolts). It ducts air from the the fan through the heater core. The heater core is in the black box with the white X on the left.

Remove radio console trim, ashtray, fascia (note screws under dash vents and at the back of the ashtray receptacle) and finally the steel supports either side of the radio. Photo shows right side support removed and lying below radio console.

Remove plastic panel under steering wheel. There are a couple of screws that you must get from below including the one in the picture at the dash light dimmer knob. The knob pulls straight off.

Then remove the duct (one screw) from behind the steering wheel under-panel.
There is a white plastic duct attached to the heater box that is connected to a black connector that directs air to the center dash vents. Below are two pictures of it (top pic shows it upside down, lower pic shows reinstalling the two pieces.) To remove, take out the screw at the base of the white duct, and the screw that connects the mouth of the black duct to the top of the center vent opening. The white duct must be pushed up to disengage the clips on the back of the heater box and then pulled away from the heater box.


Disconnect the black control cables that go to the right side (temp and fresh/recirc) from the levers they control. Disconnect the white defrost/heat/vent cable from the lever on the left side of the heater box. Then remove the 4 screws that hold the cable control panel into the dash. Push the control panel through the dash and to the left so it is out of the way.
Remove kick panels and door sill plates on both sides and peel the carpet back to expose the black plastic ducts that carry air under the front seats.
Remove the bolt that holds the duct (see first photo) and pull them down and away from the heater box.


Go into the engine compartment and drain the coolant. Remove the heater hoses from the heater core then pull the oval rubber grommets out of the firewall so that the inlet and outlet of the heater core are exposed.
Go back into the car and remove the 2 bolts (sides) and 2 nuts (top) that hold the heater box into the car. Pull and twist and it should come out the passenger side. Once out it should look like this. (BTW, don't be tempted to pull the bottom portion off (in my hand in the picture) to get the heater box in or out - it is not necessary and it is impossible to get on or off when the box is under the dash without breaking it).

At this point the bad old leaky, stinky heater core is no longer in your car and you should rejoice!