Use might or may + the base verb when something is possible but you are not sure. They mean the same (may is a little more formal). There is no to, and no -s.
might / may = maybe
I might go to the party. (I'm not sure yet)
She may be late.
It might rain this afternoon.
Not "I might to go to the party." — say "I might go to the party.". No to after might: just might + the base verb.
Try it: Take an umbrella, it ___ rain later. (might / mights / might to) Answer: might — Might never changes and takes no to: it might rain. "Mights" adds an -s that might never has, and "might to" adds a to it does not need.
might not / may not = maybe not
For a possible no, use might not or may not + the base verb.
I might not come tonight.
She may not know the answer.
They might not have time.
Try it: I'm not sure about tonight. I ___ come. (might not / don't might / might not to) Answer: might not — For a possible no, use might not + the base verb: I might not come. "Don't might" is not a real form, and there is no to after it.
sure (will) or just possible (might)?
Use will when you think it definitely happens. Use might / may when it is only possible, you are not sure.
It will rain. (I think it definitely will.)
It might rain. (Possible, but I'm not sure.)
She will pass. (I'm confident) / She might pass. (not sure)
Try it: Hiroshi looks at the timetable. The train always leaves at 9, and it is never late. He is completely sure. Which fits when he is sure? (The train will leave at 9. / The train might leave at 9.) Answer: The train will leave at 9. — He is completely sure (it is never late), so use will: The train will leave at 9. "Might leave" would mean he is not sure, but he is.
Try it: Amina hasn't decided about the party. Maybe she'll go, maybe she won't. She really isn't sure. Which fits when she isn't sure? (She might go to the party. / She will go to the party.) Answer: She might go to the party. — She has not decided and is not sure, so use might: She might go. "She will go" would mean it is certain, but she really hasn't decided.