The following are the nine common modals in English:

• can – ability, permission, possibility, request

• could – ability, permission, possibility, request, suggestion

• may – permission, probability, request

• might – possibility, probability, suggestion

• must – deduction, necessity, obligation, prohibition

• shall – decision, future, offer, question, suggestion

• should – advice, necessity, prediction, recommendation

• will – decision, future, intention, offer, prediction, promise, suggestion

• would – conditional, habit, invitation, permission, preference, request, question, suggestion

Borrowed from https://www.brighthubeducation.com/esl-lesson-plans/37641-modal-verbs-in-english/

Examples of modal usage: 

"I can go shopping tomorrow. Can you go shopping with me, Julie? "

"No, I can't (go with you). I'm sorry. What do you want to buy?"

I might buy a dress, or I might buy pants and a blouse, but I might not have enough money to buy shoes, too. "

"You should go to the Designer Mall where the prices are reduced. You shouldn't pay full price! "

"You're right! I shouldn't, should I?" 

"After shopping, I might eat lunch at the new restaurant, or I might eat at my favorite restaurant. I'll wait until tomorrow to decide."

"You might need to make a reservation, so you should decide where and when you want to eat before tomorrow!"

"You're right again! I should make up my mind about what I need to buy and where I want to eat! I'm so indecisive!"