We make sentences with "may" and "might" in the same way as with all other modal verbs:
may/might + infinitive
|Positive and negative|
I may be wrong.
He might stay.
You may not go there on your own.
May we ask you something?
How to use may and might
1. May I? = Do I have permission?
We use "may" to ask permission to do something.
May I sit here? = Is it okay if I sit here?
May I speak to Mr Norman, please? = Can I speak to Mr Norman, please? ("may" is more polite)
May she get a refund? = Is she allowed to get a refund?
We can use "may" in the meaning of permission in affirmative and negative sentences, too.
You may not speak loudly in a library. = The rules do not allow to do that.
To feel the difference between "can" and "may", remember this funny example:
— Can I smoke here?
— Of course, you can, but you certainly may not.
2. It might rain. = It is possible that it will rain.
We use "might" (and "may", but less often) to say that something is probable but we are not completely sure.
I might take a taxi or I might walk. I haven't decided yet. Both options are possible but I'm not sure what I'll choose.
Keep the phone with you. My brother might call any time. Maybe he'll call or maybe he won't call. We don't know.
Dan might not come tomorrow. He says he might have some other plans. It is possible that he won't come. Maybe he'll have some other plans. But he's not sure yet.