You can do it yourself, but it's just a bit involved. The basic procedure is the same as any other flush but there are some extra steps involved. Here's the info paraphrased from my 92 Service Manual:
NOTES:
Where it talks about the "Air Bleed Screws" be careful to not allow water to drain over the Opt-Spark! Use aluminum foil to fashion a drain to keep water away from the Opti.
For the final flushing and the re-fill of water, use distilled water. You can find it at just about any grocery store for around $.80 per gallon. Distilled water will have the minerals removed from it and helps to keep the system clean. The service manual says to add 6 cooling system pellets (a stop leak and water pump lube, but GM no longer recommends this).
Check the cooling system hoses carefully. You should consider replacing the main radiator hoses and any others that may show cracks or have soft spots. Also look between the radiator and A/C condenser for buildup of junk (leaves, dirt, small animals, Hondas, etc.) Use a garden hose with low pressure to flush out debris.
PROCEDURE:
With engine cool or cold, remove pressure cap and open radiator petcock. Open both air bleed valves (one on thermostat housing and other on throttle body, look for brass slotted screws). Remove knock sensors fro botom of block. This will get all of the coolant out as a large amount of the coolant is in the block.
Do not use a chemical flush!! If the coolant coming out is a brownish color the system must be completely flushed prior to refill of new coolant. Replace knock sensors, close radiator petcock and fill with water. When a solid stream of water comes out of the bleed valves, close them and replace pressure cap.
Start engine and get temp up 200 degrees F (93 C). Stop engine and drain as above. Do this until the water comes out clear.
After the final flush/drain, close the radiator petcock tightly, reinstall the knock sensors but leave the bleed valves open. Remove the coolant recovery tank, drain and clean it out, and then reinstall (do not refill!).
Use a "green" coolant (needs to meet GM 1825-M spec) for refill. With the system empry, slowly pour 8 quarts (7.7L) into the surge tank. Add water until a solid stream of coolant mixcome out the bleed valves. Close both valves. Continuing adding water up to the base of the neck of the surge tank.
Start engine and let it run at idle for 4 minutes. During this time, watch the coolant level in the surge tank and add water as needed so you keep the level at the base of the neck. When the thermostat opens, the water level will drop sharply so keep your eye on it. Monitor the coolant temp while you are doing this.
Add a 50/50 mix (about 2 quarts) of coolant to the recovery tank. Flush any splashed coolant from around the engine and compartment. Remember to not spray directly on the Opti!!
Keep a very close eye on the temp guage! If the temp gets up to 260, stop the engine and let it cool down. Then restart and continue the filling process. The sevice manual also says not to "attempt any agressive driving manuevers until the vehicle heats up to operating temp and cools down completely 3 times". I assume this is to insure that any air pockets are removed.
You should also see the low coolant lamp turn on after this procedure. Check the coolant level in the surge tank. The level must be right at the base of the neck for the lamp to go out.
Hope this helps!! It's sort of a messy deal to do especially with removing the knock sensors. Collect the old coolant if you can as some auto repair shops will take old coolant and recycle it.