Place your fingers on either side of the phone and gently push up on the rear case.
It is important to start from the bottom of the phone because the rear case wraps around the front of the phone at the top which makes it impossible to start prying from there.
Using a soldering iron set at 400 degrees Celsius (752 degrees Fahrenheit), heat the solder joints lateral to the headphone jack. Use a pair of tweezers to lift the headphone jack from the board.
Extreme caution should be taken when working with high-temperature equipment to reduce the chance of burns.