First, don't believe anyone who tells you that 'might' is the past of 'may'. These words are modal verbs - followed by a main verb without 'to' - so they don't work like ordinary verbs, and the idea of past or present doesn't really help you.
In many cases they are interchangeable. They introduce the idea of uncertainty and supposition/hypothesis - or in other words, they tell you that the speaker isn't sure about something. As a general rule, 'might' is a bit more uncertain (or 'tentative') than 'may'.
Here are some examples:
'May' is used with in first person only (I, we) for polite requests.
eg May I ask you a question?
May we come in?
Might is used for possibilities (may is possible here, but less usual)
'I might come to the party tonight, but I'm not sure. It depends whether I finish my work early enough'
It can be used for guessing eg
'I don't know where John is. He might be still at work'.