To get rid of a cyst on your eyelid, wash your hands thoroughly with soap and wet the corner of a clean washcloth with very hot water. Next, apply one or two drops of baby shampoo on the wet corner and rub to produce suds. Then, scrub gently along the edge of your upper and lower eyelid, inside the lash line of the affected eye. After that, rinse the washcloth corner thoroughly with hot water and run it over your eyelid edges. Finally, dry your face with a clean towel. This should be done for some time.