Must and have to are modal verbs often used to convey necessity.
- I have to go home now.
- I must arrive by 12.00.

Have to is used for general necessity. For example:
- I have to finish this before 12.00. (I have a general obligation to finish this by 12.00)
Must is used for necessity which we feel personally.
- I must finish this before 12.00. (I have a sense of strong personal responsibility to finish this.)

Must does not have a past form, we have to use have to for the past.
- I had to get up early this morning.
- I must got up early this morning. This is incorrect.

Note that have to inflects like a normal verb, it can have different tenses and uses auxiliary verbs for questions and negatives. For example:
- Do we have to go out tonight?
- You don't have to come with us.

Must doesn't use auxiliary verbs or different tenses.
- Must we go out tonight? (This sounds rather British, I really don't want to go out tonight.)
- We mustn't forget the tickets. (No auxiliary verb "to do", just add not.)

Don't have to means that something is not necessary, but possible.
- You don't have to come, but you can if you want to.
- We don't have to leave today.

Must not is strong and means that something is prohibited.
- You must not push the red button.
- We mustn't be late.

Must and have to can also express certainty.
- This must be the ight way.
- This has to be the right way.

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