can to express ability I can speak a little Russian.
can to request permission Can I open the window?
may to express possibility I may be home late.
may to request permission May I sit down, please?
must to express obligation I must go now.
must to express strong belief She must be over 90 years old.
should to give advice You should stop smoking.
would to request or offer Would you like a cup of tea?
would in if-sentences If I were you, I would say sorry.
A modals quiz.
More explanation here.
More practice here.
Here are some safety dialogues.
On page 66, there is a story about an accident.