If you have determined that the offending matter is stuck under your upper eyelid, open your eye as much as you can while gently pulling your upper eyelid away from your eyeball. Slowly close your eye while keeping the upper eyelid extended and try to keep it far enough out to cover the lower eyelid. Then release your upper eyelid and gently open your eye. Chances are your eyelashes will catch the offending item and sweep it out of your eye.
If the item is under your lower eyelid, gently pull the lower eyelid away from the eyeball as much as you can so that you can seek the bit of trash. Often whatever it is will be moved to the juncture of your eyeball and the inside of your lower eyelid when you pull the lower eyelid away from your eyeball. At that point use the corner of a clean handkerchief moistened with some water to gently sweep the material out of your eye. You may also use a moistened cotton swab but press gently or you may damage your cornea by the swab instead of the trash, or both.
Another method I read about in Mother Earth News is for one person to hold the eyelids of the person needing assistance as far apart as possible then gently lick the irritated eye with the tongue. The saliva does not cause any irritation to an eye by itself, the tongue is soft enough to not physically damage an eye and the texture of a tongue is enough to get a grip on whatever it is to lift it out of an eye.
I do not use this last method as I'm surprisingly squeamish about it but, it can work
. I mainly use the lash sweep method or the cotton swab method, they work just fine for me. 