Use a grinder to sharpen a sports-ball inflating needle by making a steep angle from one side of the needle to the other. In this way, the point is on one side of the needle as opposed to in the center where the hole is. Sharpen it enough so that you can easily puncture a PET soda bottle with it.
Insert the threaded end of the needle into one end of some rubber tubing so that you have a good seal.
Put the other end of the tubing in a graduated measuring cup full of water. Turn the measuring cup upside down in a tub of water, being careful not to let any air enter. The measuring cup should have nothing but water in it.
Place a bottle of soda in a pan of water on a hot plate. The pan of water is necessary to prevent the bottle from getting too hot and melting.
Puncture the neck of the bottle with the inflating needle so that the tip of the needle is in the soda's head space. Make sure nothing is obstructing the flow of carbon dioxide into the tip of the needle. Use rubber cement to seal the hole in the bottle around the needle.
Turn on the hot plate to a low setting to keep the water from boiling. Carbon dioxide is less soluble at higher temperatures, so after an hour of heating, most of the carbon dioxide should be driven out. The gas will displace the water in the measuring cup so you can measure its volume.