To remove a stuck earring back, called a clutch, wash hands with antibacterial soap, and then rub a small amount of petroleum jelly on the backside of the earring. Once it's lubricated, firmly hold the front of the earring in place, and gently turn the clutch to loosen it.
If the clutch won't loosen by turning it, try wiggling it back and forth gently to get it realigned on the post. If it's especially difficult to grip the clutch, hold the earring firmly, and try grabbing the clutch tightly with tweezers to pull it off the post. If the piercings are new, use a cotton swab to clean the piercing area with a sterile solution such as hydrogen peroxide before attempting to remove the earring.