If your character sounds too good to be true, then it is probably a Mary Sue. If your character always seems to be in the middle of everything and is always the one to resolve any issues/problems, then it could be a Mary Sue. If your character is more attractive/powerful/impressive than any other character by a mile, then it is probably a Mary Sue.
Unless your story is specifically about super-heroes, your character should not exhibit supernatural tendencies. Also, if you find yourself relating very closely to the character and feel that you are modeling it after your own traits/preferences/ideals, then you are definitely leaning towards a Mary Sue!
Basically, just evaluate whether or not your character is realistic. If it seems to be instilled with any form of talent that gives it an unfair advantage over other characters, then you need to tone it down.
One more important note: simply being aware of this pitfall goes a long, long way towards avoiding it in your own writing. Once you're sufficiently aware of the effect, with any luck you'll know it when you see it.