should is a suggestion.
must a more individual rule to follow, whereas "have to" a general rule is. Pay also attention that must does not have a future/past tense. You have to (^^) use "have to": You must do your homework! = I had to do my homework.
Since I am not sure whether you ask for English or German...here the same for German:
must/have to = müssen (a command - ein Befehl)
Kinder müssen in die Schule gehen = Children have to go to school.
Sie muss ihr Zimmer aufräumen = She must clean her room.
In a more formal and old-fashioned way, German has also the "haben"-structure:
Er hat dies zu tun. = He has to do it.
In colloquial German this is usually not used.
should
sollen = suggestion - ein Vorschlag
He should go to the doctor = Er sollte zum Arzt gehen.
We can emphasize in German more than in English by using also "Konjunktiv":
Er soll zum Arzt gehen
Er sollte zum Arzt gehen.
The first sounds more like a command. Actually, it is one. But weaker than "Geh zum Arzt!".
The second is more a suggestion.
You will find "man soll/sollte" in many talks and texts. It is a very colloquial expression, and sounds a little unimaginative and "uneducated". You should avoid it. You will find such expressions like: "Man sollte dies hier drücken. Man sollte dies öffnen". You should clearly state what you want: "Drücken Sie den Knopf!" or "Öffne dies hier"...