Plug the sink with a stopper, and run a basin of hot water that will cover all but 1 to 2 inches of the outer bottle. The water should be hot but not boiling. The hottest tap water available should suffice.
Put on kitchen gloves to protect your hands from the hot water.
Drop several cubes of ice into the inner bottle to maintain its temperature.
Place the bottles down into the hot water and wait 10 to 15 seconds. Try to twist the outer bottle gently. If this is not effective, wait another 10 to 15 seconds and try again.
Turn the bottles sideways and pull them apart when the outer bottle can be turned.