modal: The auxiliary verbs or helping verbs such as will, shall, can, would, could, should, might, may, and ought to. Some authors consider have to, need to, and used to to be semi-modals, but they lack some or all of the structural properties of modals. Structurally, modals have several properties (Have to is compared in brackets).
Modal rule 1: They do not have a third person plural 's'.
I can swim. She can swim. (I have to go. She has to go).
Modal rule 2: They invert in questions.
I should go. Should I go? (I have to go. Do I have to go?)
Modal rule 3: They do not require do for emphasis.
You could do it. You COULD do it. (You have to do it. You DO have to do it.)
Modal Rule 4: They cannot be linked.
I will must do it. (I will have to do it).
Modal Rule 5: They have their own negatives.
I couldn't call him. (I don't have to call him).
Modal Rule 6: Ellipsis
I can do it and so can you. (I have to do it and so do you).
Semi-modals pose problems for classification. Consider the semi-modal need. Need I go? He needn't call you. Clearly, it can behave like a modal.
Functionally, modals have several meanings each.
Can can be used to show permission, ability, or possibility.
Can I go? I can swim. It can happen.
Must can be used to show certainty or obligation.You have been working all day so you must be hungry. You must work harder.
For a discussion on teaching modals see: Modal ESL Activities.