The method I have used for years depends on a thing that was sold to me as a "filling device" pictured at
http://www.pbase.com/image/122950815. I now use it with Sankey kegs but filled many a Corny with it in the past. The tube goes to the gas out port of the target keg which is best prepared by filling with a no-rinse sanitizing solution (or sanitizing solution which is then replaced with boiled rinse water). The fill should be complete i.e. no air left. The liquid is then pushed out with CO2 and pressurized to above the pressure in the source keg. You now have a keg with no air whatsoever at postive CO2 pressure. Connect the gas out on the target keg to the device and the liquid in to the source keg or fermenter but don't open the beer valve yet (or push the connecter down on the post or seat the couple). First use the needle valve on the device to bleed off the pressure in the target keg to slightly less than the pressure in the source. Then crack the valve or seat the connector or coupler. You should verify flow in the correct direction. You do not want to be forcing CO2 back into the source keg as it will disturb the sediment in the source keg. If the beer in the source keg has been fined or filtered this is not so much a concern.
Once you have verified flow you can regulate the flow rate by how far you open the device needle valve. It is best to have the target pressure only a pound or 2 below the source as otherwise the beer will flow too fast and foam up. You can verify what the source pressure is in this context by closing the needle valve completely. Beer will flow into the target until the pressure in the target just equals the pressure in the line which you then read from the device's pressure gauge. The reason it is better to do this than just read the gauge on the CO2 tank feeding the fermenter or source keg is that these gauges aren't exactly precision instruments.
It's great if you can place the target keg on a scale. That way you can monitor the filling though you can also do that by placing your hand on the side or top of the target keg. When the cold beer reaches the level of your hand you will feel the cold through the keg wall/dome.
A lot of people "purge" their kegs of air by filling with CO2, bleeding and refilling/bleeding one or more times. Working an example shows why this is not as effective as complete displacement with liquid or another gas (I use steam on Sankey's). Starting with a keg full of air at atmospheric pressure the partial pressure of oxygen is 0.2 atm. Now pressurize to 30 psig (3 atm) with CO2. The partial pressure of O2 is still 0.2 atm and the mixture after it stabilizes, is thus 0.2/3 = 6.66% O2. Bleed back down to 1 atm and you have 0.066 atm partial pressure of O2. Better than 0.2 but not that great. Repeat and you will have 0.066/3 = 2.2% O2 which, bled back to 1 atm contains 0.022 atm. A third pressurization/bleed cycle will get you to 0.007 atm and so on.
Who leaves their precious beer along during a transfer?
