How To Use May and Might

May

We can use 'may' to ask for permission. However this is rather formal and not used very often in modern spoken English

* May I borrow your pen?
* May we think about it?
* May I go now?

We use 'may' to suggest something is possible

* It may rain later today.
* I may not have time to do it today.
* Pete may come with us

Might

We use 'might' to suggest a small possibility of something. Often we read that 'might' suggests a smaller possibility that 'may', there is in fact little difference and 'might is more usual than 'may' in spoken English.

* She might be at home by now but it's not sure at all.
* It might rain this afternoon.
* I might not have time to go to the shops for you.
* I might not go.

For the past, we use 'might have'.

* He might have tried to call while I was out.
* I might have dropped it in the street.

taken from: http://www.englishgrammarsecrets.com/maymight