English Basic Modal Verbs

Modal verbs and modal auxiliary verbs are verbs that are typically used in combination with another verb in the infinitive.
A modal verb typically follows the same conjugation for all personal pronouns, and do not have the third-person-s.
The most common modal verbs are: can, could, may, might, shall, should, would, ought to, must, will, used to. 

Other modals and modal auxiliaries do have the third-person-s when conjugated. Examples are: need, have to.

May – Might – is used to signify a possibility

Examples:
I might go skateboarding. He/She might go skateboarding.
We may join you tomorrow. He/She may join you tomorrow.
They might be late. He/She might be late.

Can – Could – is used to signify the ability or the possibility

Examples: 

I can read.
He can speak three languages.
We could go out tomorrow.
She could not find her purse.

Must & Must not  

I must (do something) = I need to do something/I am expected to do something. 
I mustn’t/must not do something =  I am not allowed to/shouldn’t do something, it is the wrong thing to do. 

The modal verb “must” is typically used with another verb in the infinitive, omitting the preposition “to”.

Examples: 
I must (modal verb) call (verb in the infinitive) my friend.
You must (modal verb) be (verb in the infinitive) very tired!
She must call the doctor. He must take the train.

You mustn’t (most not – modal) be (inf.) so hard on yourself! (You should not be so hard on yourself)
You mustn’t (modal) tell (inf)  anyone about this! (def: You are not allowed to tell anyone about this!)

Have to

The modal auxiliary verb “to have to” signifies something similar to “must”, and is commonly used when someone needs to or is expected to do something. Unlike “must“, “have to” can be used in the past, simply by using “had to“. There is no past-form of “must”. When conjugated, “have” changes to “has” in the third person singular.

Examples:
I have to get up early tomorrow. She has to get up early tomorrow.
I had to get up early for my flight last week.
You have to be very careful. He has to be very careful.
She had to cancel her appointment last Friday.

To use “have to” in the negative, we need to use “to do”.
I don’t have to get up early tomorrow. She doesn’t have to get up early tomorrow.

Need to  

The modal verb “need to” is used to signify that something is important, but not absolutely necessary (for which we would use “must” or “have to”. Just as “have to”, “need to” can be used in the past, using “needed to”. We need to add an “s” for the third person singular.

Examples: 
I need to go to bed soon! (It is not an obligation, but it is strongly needed) She needs to go to bed soon.
We need to buy eggs at the store. He needs to buy eggs at the store.

They needed the answer by noon yesterday.
I needed flour and milk for the recipe.

Should 

“Should” is used to signify that is would be appropriate, or suggested to do something, but it is not a necessity or an obligation. The modal verb “should” is used with another verb in the infinitive, but without the preposition “to”. There is no third-person-s.

Examples:
I should call my parents more often.
He should eat more vegetables.
We should go to the concert next Friday.
They should offer vegetarian options on the menu!

Like “Must”, there is no past tense form of “should”. However, it is possible to use “should” in the past, by using it in combination with the Past Participle.

I should have called my parents more often.
You should have eaten more vegetables.
We should have gone to the concert last Friday.
They should have offered vegetarian options on the menu!