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We use the modal verbs "may" and "might" to talk about possible activities or happenings in the future:

• I'm not sure I'll go to the party. I may be away.
• Don't drop by at 7:20 PM. I might be watching TV.
• Please, prepare something to eat. Mr. Johnson might be hungry.
• We may not be able to go to school this week.

There isn't much difference between the two. So you can say:

• "John might be at home" or "John may be at home".
• "I may visit Mary" or "I might visit Mary".

Sentences formed with "might" are less likely to happen than those with "may". For example:

• I may be away at 10 PM. (35% likelihood)
• I might be away at 10 PM. (20% likelihood)

However, when the situation is unreal, only "might" can be used:

• If I were a bit smarter, I might go to college. (The speaker won't become smarter, so the situation is unreal)

If you want to emphasize progression of a situation, you may use the continuous form of the verb after the modal.

• Don't drop by at 7:20 PM. I may/might be watching TV.

If you're using the reported speech, "may" becomes "might".

• "I may be late," said Frank. In reported speech: Frank said that he might be late.

Read about Modals in the Reported Speech.