If you find out some certain person is angry at you -how long would take for you trying to guess what you did?

Oh my life in a nutshell. Ha!

I'd most likely have a rather qualified hunch why they were mad at me. My senses work that way. There will always be exceptions.

Half an hour.

Depends on the person.
With someone close and important, instantly or at the first appropriate moment.
With someone I don't know well enough, or fear, perhaps never - would more likely walk away.

I usually have some sense that someone is not happy with me.  If I don't, they are playing me real well. 

I would have to have a little discussion with them and explain why they're completely in the wrong to be angry at me. 

Anger is a secondary emotion.
Underneath it is one or more of three primary emotions: pain, fear or shame.
I scan my memories to check if anything I said or did could have triggered those responses in the other.
If I can't see any that are obvious, then I need to ask the other how he or she is feeling, what triggered it and what the need or request is.
I regard this as a process that is valid for friendships, husband, anyone close.
Time depends on privacy and the other's priorities but I find that the sooner the better because most people seem very forgetful of details.