Unfortunately, there is no real DIY way to fix a Home Button, only Apple can replace it.
You will need to carefully inspect the Home Button and flex to see if there is any damage. Magnification here will help. Look for tears to the flex or any physical signs of damage. Also inspect the flex that runs under the LCD Heat Shield as it tends to tear at the corner. You should also check the connector to insure none of the pins are damage or that there isn’t any debris.