Modals

Utilizamos los verbos modales para expresar precisamente eso, la “modalidad“, es decir, la actitud del hablante respecto a la acción enunciada. Si dices “She can’t arrive in time“, estás indicando que crees que es imposible (actitud, opinión) que ella llegue a tiempo (acción). Aquí tenéis una tabla que resume los principales modales, aunque faltan needn’t (indica que algo no es necesario, no hace falta) y had better (conveniencia, “sería mejor”); ambos aparecen en vuestro libro y en los enlaces que tenéis más abajo.

Modal	Usage	Example
can	ability	I can do several things at the same time.
	when something is possible	Miracles can happen.
	permission	You can go now.
	informal requests	Can you come here for a minute?
could	past form of “can”	She said she could pay for us as well.
	polite requests	Could you move your bag, please?
	possibility	It could be that he missed the train.
may	possibility	It may rain tomorrow.
	ask for or give permission (formal)	May I speak?
might	past form of “may”	He said he might change his mind.
	possibility	This might fail.
must	you have to do it	You must obey the law.
	it’s very logical or very likely to happen	They left so early, they must be home by now.
must not/ mustn’t	you are not allowed to do it	You mustn’t smoke in here.
shall	future for “I” and “we”	I shall see him tomorrow.
	questions and suggestions for “I” and “we”	Let’s continue, shall we?
should	the right thing to do	She should call the police.
	advice	– What should I do? – You should stop thinking about it.
	what is likely or expected to happen	We should be back by midnight.
will	future action or states (not plans)	Prices will go up next summer.
	promises and intentions	It’s alright, I’ll pick it up.
would	past form of “will”	He told me he would come.
	imagined situations	What would you do if you were him?
	for polite requests, offers and invitations	– Would you please sit down? – Would you like some tea? – We are meeting with Sarah next Saturday, would you like to come along?
	to say what you want to do or have	I would like a piece of cake.
ought to	the right thing to do	You ought to apologize.

Aquí tenéis otro resumen interesante, muy claro, con ejemplos y con colorines (aunque también omite el had better) y aquí, el tutorial más completo que he encontrado en la red, con explicaciones y ejercicios de cada verbo (y que es el que os recomiendo seguir).
Sobre “had better“, aquí tenéis una explicación muy buena en flash (con animación y sonido) y aquí por escrito y con ejercicios.
Quien lo lleve peor, puede empezar por el post de la ESO, hacer sus ejercicios (muy sencillicos) y volver luego aquí.