Nail glue is cyanoacrylate -- otherwise known as super glue or crazy glue. Whatever you call it, it's a quick-bonding, strong adhesive, and it bonds permanently. This sounds like bad news for your clothing, but for all its strength, cyanoacrylate has an Achilles heel: Acetone. That's the main ingredient in nail polish remover, so if you're gluing your nails, it's a safe bet you have some around. If you don't want to risk discoloring the fabric, there's always soap and water.
Procedure for Removing Nail Glue
Moisten a cotton swab with paint-grade acetone. You can also use nail polish remover if perusal of the label reveals that it contains acetone; if so, use the applicator in the bottle instead of a cotton swab.
Dab the dried glue, being careful to avoid the surrounding fabric as much as possible. The glue should soften.
Peel the glue away from the fabric carefully with tweezers or a knife. If the fabric is acetone-safe, use an old toothbrush to brush away the glue.
Wash the fabric in the laundry to get rid of residue and odors.
Soap and Water Method
Soak the garment in a basin filled with cold, soapy water.
Scrub the stain with a toothbrush until you've removed as much of the glue as possible. If you need more scrubbing power, dip the toothbrush in laundry detergent.
Rinse the fabric in clear water, then put it in the laundry with the rest of your clothes and wash with a good quality laundry detergent.