Notice that this person is always hanging around with you lately and calling, writing you notes or emailing you just to say "hi." If a person fancies you, they won't be able to stay away from you.
Notice if this person is coming to you for advice and really listening and taking your responses to heart. If you go on a date with someone else, see if this person seems bummed out instead of glad for you.
Pay attention to when you go out in a group. See if this person is always the last to leave you and is always by your side, laughing at your jokes.
Note if this person seems to melt or get nervous if you ask them out and gets flustered/blushes/responds enthusiastically if you hug or kiss them goodbye.
See if close friends of yours have noticed and commented that this person seems to really fancy you. Sometimes your friends see things that you are blind to seeing.