Replace Heater Core on a Corsica

This job is easier with the Corsica than it is with many cars, because removal of the dashboard is not required.

Steps

Put the front of the car up on ramps or jackstands, and block the rear wheels. Set the parking brake.
Drain the cooling system after removing the radiator cap. Later-model Corsicas also have a pressure cap built into the overflow reservoir. Remove this cap if this is the case. Put a drain pan under the radiator drain. If the coolant is in good condition, reuse it.
Working under the car, remove the hoses from the heater core. This would be a good time to replace the heater hoses if they are old. Hoses that have deteriorated won't seal to the new core.
Plug the now-open ends of the core.
Working inside the car, remove the console if it hinders removal of the access panel to the heater core. In the case of some models, this step is not necessary.
Cover the work area with newspapers or rags to prevent spillage of antifreeze on the carpet.
Remove the access panel, which is directly under the instrument panel center. It's a black plastic panel that is about six by twelve inches and held with about six screws.
Remove the strap holding the core to the heater box and remove the core.
Installation is the reverse of removal.
Refill the cooling system and lower the vehicle. Make sure that the level is at the full-cold mark. Check the level after a day to make sure the level is correct; sometimes air will get in the lines, and you will need to add more coolant.

Discard old spring clamps on hoses, and replace with screw clamps. The old ones are a one-shot deal.
Run the engine when topping off coolant and run the heater. Normal heat flow inside the car will indicate that you have enough coolant and that there is coolant in the core.
Be sure to close the drain valve after you finish draining the cooling system. This will prevent wasting coolant.

Do not use any antifreeze except the type recommended by the vehicle's manufacturer. Mixing or using the wrong type can cause leaks and corrosion.
Working in the vicinity of the airbag can deploy it, possibly resulting in personal injury. For this reason,the battery's negative cable should be disconnected prior to doing any work on or under the dash.
Never work on a car that's supported only by a jack. Use the safety stands mentioned in Step One above, as a jack can fail.
The engine must be completely cool before beginning any work on the cooling system, and this includes the heater core.

Antifreeze and distilled water (or a quick fill kit, as described in your owner's manual), rags and newspapers, a drain pan, new clamps and possibly new heater hoses.