You don't have to have the machine. If you read that article till the end you'll see that it describes also the "old way" of doing it. It is exactly as Wayne written. In fact you don't have to reach for the plug. Just disconnect the upper hose from the radiator, connect the clear hose and run the engine only for 15-20 seconds, than you'll see the bubbles in the hose. Stop, put 2 quarts of oil, start the engine again. You should do this until the fluid in the hose becomes clear pink. It usually takes 14-16 quarts of oil. Try changing it to synthetic if you don't mind the doubled price for the oil.
ihsan