We use must to express wishes, desires and intentions of the speaker and his/her interlocutor.
I must do it. (I want to do it.)
I must start working right now. (I want to do it.)
It's very late. We really must stop playing. (It's our intention.)
We use have to to express external obligation.
I have to do it. Teacher's orders.
I have to start working right now. My boss tells me to do it.
It's very late. We have to stop playing because we'll be late for dinner.
But remember that mustn't expresses prohibition. Don't have to expresses something that is not required.
Children mustn't play with fire.
I don't have to work next Saturday.
We use should to express a suggestion, an advice. It is weaker than must and have to.
You should save some money.
You shouldn't smoke so much.
Now, try some practice.