Use the point of a spudger to carefully separate the home button cable from the adhesive securing it to the front panel.
If the cable doesn't separate easily, apply heat using an iOpener or hair dryer to soften the adhesive, and try again. Be careful not to damage the cable.
Once all the adhesive has been separated, remove the home button from the front panel.
If you are replacing a broken front panel, there may be glass shards stuck to the home button. Carefully remove any remaining glass before transferring your home button to a new display.
Your replacement part may come with an extra Phillips screw already installed left of the Home Button. Remove the unnecessary screw so that you can reinstall the home button bracket.