Methods for brewing compost teas date back to early Roman, Greek and Egyptian times (Brehaut, 1933). Early methods consist of simply a bucket, compost, water and occasional stirring. However methods such as these create high probability of anaerobic conditions developing.
As a result plants died when the tea is used. As time has moved on and with a better understanding on the science behind compost teas, there are now many different ways to create good quality and consistent teas by using aeration, correct food source and good quality composts!
There is a great guy called Bruce Deuley who knows a lot about current methods of brewing compost tea. You can see his seminars on Youtube.