From real simple:
Follow These Two Easy Steps
a sewing needle, push the scraggly bit of the snag through to the
inside of the sweater. If the snag’s too big to grab
this way, turn the sweater inside
out and use a crochet hook to tug the strands to the inside.
Tip: Don’t cut the snag’s strands; you might create a hole.
Keep the snag at bay by tying it in a knot. Dabbing the knot with clear nail polish will stop it from unraveling, but make sure the knit is thick enough to prevent any polish from bleeding through to the sweater’s front.