Modal verbs

English, in common with other languages, has a series of "helper" or "auxiliary" verbs.

They are the auxiliary verbs to be, to have, to do and the modals, would, will, can, could, shall, should, may, might, must and - an odd one - ought to.

The difference is that the helper verbs to be, to have and to do change according to the  person and tense:   I am going, he was laughing, we were running, he is driving, does he smoke?, do you like?, did he try?, I have worked, he has suffered, she had  thought; whereas the modal verbs do not change: I will drive, he will read, they should try, we would offer, he might eat, I couldn't care less, you may open.

That's it, really.

Modals are those little words that do not change.
I must/may/might/should/shall/should/will/can/could go;  
She must/may/might/should/should/will/can/could go.

One thing to remember is that a verb in English is usually made up of an auxiliary/modal and a main verb.  In the sentence He may have been sleeping, the verb is actually  made up of four parts (as underlined); in the sentence By the time I die, I will have worked unhappily in the office all my life, it is made up of three; in the sentence You should work more, it is made up of two.

If a verb is made up of just one part -- without, therefore, an auxiliary or modal --  it forms what is known as a "simple tense": I cook, he chews, they went.