Hi,
You get a bucket or other container...release your fish or coral from the bag and take an air line tube and tie a knot in it to be able to adjust the water flow drip...(or use an IV line) and syphon the water from your aquarium into the bucket a drop at a time. Using this method, I have found that the temp in the bucket, is not the same as the temp in the tank. That's why I don't use this method.
To me, even though SWfish.com says to use the drip method...it's a pain in the butt. I float the bag for a little bit so the temps are the same, then open it (I roll the bag opening to keep it afloat), and using a turkey baster, I remove some water from the bag and dump it in a cup...then take a little water from the tank (it should be a quarantine tank) and squirt it into the bag...I do that every 15 minutes, for an hour to 2 hours depending on the critter. By the time your done, only water from the tank is in the bag for the most part, and I release the fish, water and all. If you ask 20 people, you will get 20 different answers...everyone has their own way. I never lost a fish doing it this way.