Which cooling system are you talking about? Hell Ill post both
Engine cooling: keep the cap off the overflow tank and turn the car on. Turn the heat all the way up and the air to high. Fill the overflow tank as needed. It will take anywhere from 2-5 times to get it all out and even then I add a little more than the top to make up for little bubbles etc. Usualy after 10 minutes of running or so its enough for that particular run.
Air conditioning is easier. Just rent an air pump from autozone for free and attach it to the low side line input (where you put refrig to refil on the passenger side close to the radiator) and have it pull I think 24 pounds of pressure for 1 hour. Refil and your done. If you don't have an autozone but happen to have an air compressor you can get a venturi vacuum puller for like $10 at harbor freight or online.
Hope this helps!