1.-They are auxiliary verbs. They don't require the auxiliary 'do' in their negative or interrogative forms:
-He shouldn't go shopping so often
-Can you speak English?
2.-We add 'not' to form the negative:
-We shouldn't go to that party.
-You mustn't smoke here.
3.-No 's/es' for the 3rd person singular:
-She must study harder for the exam.
-He should go to the dentist.
4.-They are followed by the infinitive without to (except for 'ought to'and 'have to'):
-She should visit her grandmother.
-I could swim when I was 4.
5.-They don't have an infinitive, an -ing form or a past participle.
6.-They convey an attitude or mood: