How to replace the heater core

You got lucky on this one. The dash doesn't have to come out

Remove or Disconnect

1. Negative battery cable.
2. Drain cooling system. Refer to: See: Cooling System > Procedures
3. Raise vehicle.
4. Drain tube from heater case.
5. Heater hoses from heater core.
6. Lower vehicle.
7. Console (if equipped).
8. Right and left sound insulators.
9. Steering column opening filler.
10. Floor air outlet duct.
11. Heater core cover.
12. Heater core mounting clamps and remove heater core.

Install or Connect

1. Heater core and heater core mounting clamps.
2. Heater core cover.
3. Floor air outlet duct.
4. Right and left sound insulators.
5. Console.
6. Steering column opening filler.
7. Raise vehicle.
8. Heater hoses to heater core.
9. Drain tube to heater case.
10. Lower vehicle.
11. Negative battery.
12. Fill cooling system and check for leaks. Refer to: See: Cooling System > Procedures

See the diagrams below for component locations described above

Use the car repair manual link in the thread or get a Haynes manual.
Some are easy to replace, some you have to remove a good portion of the dash.

HEATER CORE

REMOVAL
Disconnect battery ground cable.
Drain cooling system.
Raise and support vehicle.
Disconnect heater hoses from heater core assembly.
Remove drain tube.
Lower vehicle.
If equipped, remove console as follows:
Apply parking brake and block drive wheels.
Position transaxle shift lever in Neutral.
On models with automatic transaxle, remove clip retaining shift lever handle to lever, then remove shift lever handle.
On models with manual transaxle, turn shift lever handle counterclockwise to remove from lever.
On all models, carefully pry upward on outer edges of console trim plate.
Disconnect electrical connectors and ashtray lamp from console trim plate, then remove trim plate from console.
Remove console to mounting bracket attaching screws, then remove console.
Right and left sound insulators.
Steering column opening filler.

Floor Air Duct Outlet

Floor air outlet duct.
Heater core cover.
Heater core mounting clamps and remove heater core.

INSTALLATION
Heater core and heater core mounting clamps.
Heater core cover.
Floor air outlet duct.
Right and left sound insulators.
Console.
Steering column opening filler.
Raise vehicle.
Heater hoses to heater core.
Drain tube to heater case.
Lower vehicle.
Negative battery cable.
Fill cooling system and check for leaks.

FIG. 2

Removal & Installation

1.Disconnect negative battery cable.
Drain cooling system.
Raise and support vehicle.
Remove drain tube.
Disconnect heater hoses from heater core.
Lower vehicle.
2.Remove console (if equipped).
Remove left and right sound insulators from below instrument panel.
Remove floor outlet duct.
Remove heater core cover and heater core.
. To install,
reverse removal procedure.
Fill cooling system

HEATER CORE

REMOVAL
1.Disconnect battery ground cable.
2.Drain cooling system.
3.Raise and support vehicle.
4.Disconnect heater hoses from heater core assembly.
5.Remove drain tube.
6.Lower vehicle.
7.If equipped, remove console as follows:
a.Apply parking brake and block drive wheels.
b.Position transaxle shift lever in Neutral.
c.On models with automatic transaxle, remove clip retaining shift lever handle to lever, then remove shift lever handle.
d.On models with manual transaxle, turn shift lever handle counterclockwise to remove from lever.
e.On all models, carefully pry upward on outer edges of console trim plate.
f.Disconnect electrical connectors and ashtray lamp from console trim plate, then remove trim plate from console.
g.Remove console to mounting bracket attaching screws, then remove console.

8.Right and left sound insulators.
9.Steering column opening filler.
Floor Air Duct Outlet

10.Floor air outlet duct.
11.Heater core cover.
12.Heater core mounting clamps and remove heater core.

INSTALLATION
1.Heater core and heater core mounting clamps.
2.Heater core cover.
3.Floor air outlet duct.
4.Right and left sound insulators.
5.Console.
6.Steering column opening filler.
7.Raise vehicle.
8.Heater hoses to heater core.
9.Drain tube to heater case.
10.Lower vehicle.
11.Negative battery cable.
12.Fill cooling system and check for leaks.