Relationships between opposite sex friends

Well, do not ask the person directly but concentrate on watching how the other person reacts in different situations - e.g. in your presence, in the presence of people you are sure s/he dislikes, in the presence of people you are sure s/he likes and compare. Watch what s/he says directly to them and watch if that speech coincides with what s/he really thought about them in that moment. 

Read a few books about non-verbal communication - body language, voice variations, etc. Those so called non-verbal clues can be revealing.

I think drabsv had some great suggestions, nothing more I can add

It depends on how comfortable you are with that friend, but maybe go through her/his friends and ask. Also, if you do feel awkward, then it isn't meant to be.

There is no way to know for sure without risking getting hurt or harming the firendship, but if you really feel attracted to this person and you feel you can not go on simply as friends, that your romatic feelings get in the way, you can say, "Gee, I feel attracted to you and I was wondering if you felt the same way." If you are simple curious and have no interest in a relashionship, it's better not to bring it up just to validate your own attrativeness.

Being wise,and sensible should give it the best approach.Trick him/her and let her/him get annoyed completely,this is when you will realize if he can have some feelings for you.