The main modal verbs are
can, could, must, may, might, should, shall, will and would.

Its most important characteristic is that "to" is not used between the modal verb and the main verb. For example, with the common verb "to want" we would say "I want to go.", but with the modal verb "can" the correct word would be "I can go.", without the "to" in the middle.

Another feature is that, to ask a question with a modal verb, simply invert the subject with the verb - that is, if the statement is "You can go.", the question will be "Can you go?".

Let's see their meaning one by one:

Can

 

The modal verb "can" generally means "to be able" or "to be able to" do something. I can go there with you. (I can go there with you.) Can you cook tonight? (Can you cook tonight?) It can also be used to talk about skills and things we know how to do: Can you swim? (Can you swim?) We have a specific article for the modal verb can in English where you can see more examples of its use.

Could

 

The modal verb "could" has two different meanings. The first would be the conditional of "can", something that would be like "poderia" in Portuguese. It is often used in questions as a more formal and polite version of "can". Examples: Could you help me? (Can you help me?) I could do the dishes for you if you gave me some money. (I could wash the dishes for you if you gave me some money.) The other meaning is the past tense of "can", something like "podia" or "pude" in Portuguese. Examples: I was too busy and couldn't come to the party. (I was too busy and couldn't come to the party.)

Must

 

The modal verb "must" generally means "must" or "have to" do something, in this sense of obligation. It can also indicate "ought" in the sense of an assumption. Examples: I must go home soon. (I have to go home soon.) He must be very rich. (He must be very rich.) We have a specific article for the modal verb must in English where you can see more examples of its use.

May

 

The modal verb "may" in English expresses the possibility of something being accomplished: I may go to the party. (I can go/maybe I will go to the party.) It can also have the meaning of giving or asking for permission: You may not use the car tonight. (You can't use the car tonight.) We can still translate it as "power", just like "can", but its use is much more formal: Teacher, may I ask a question? (Teacher, can I ask you a question?) May I take your order? (Could I take your order?) We have a specific article for the modal verb may in English where you can see more examples of its use.

Might

 

The modal verb "might" is very similar to "may" in the sense of expressing the possibility of something being accomplished. However, it expresses a less likely possibility than "may". Examples: I might go to the party. (I can go/maybe I will go to the party.) It might rain tonight, but I don't think it will. (It might rain/maybe it will rain tonight, but I don't think it will.) However, unlike "may", it is not usually used to ask for permission.

Should

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The modal verb "should" is generally used to give advice, something that would be like "should" in Portuguese. It's like a softer version of "must". You should go there. (You should go there.) I should leave you alone. (I should leave you alone.) It can also be used to ask someone their opinion or make suggestions: Should we look for a place to eat? (Shall we look for a place to eat?) We have a specific article for the modal verb should in English where you can see more examples of its use.

Shall

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The modal verb "shall" can also be used to give or ask for advice or a suggestion. It tends to be used less than "should". What shall I do? (What should I do?) Shall we go? (Shall we go?/Should we go?)

Will

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The modal verb "will" will most often be used to form the future in English. I think I will move to Brazil. (I think I'm going to move to Brazil.) He will probably be tired after work. (He'll probably be tired after work.) It can be abbreviated as " 'll": I think I'll move to Brazil. (I think I'm going to move to Brazil.) He'll probably be tired after work. (He'll probably be tired after work.) It can also be used in a more colloquial way to make a suggestion or make a request: Will you help me? (Will/can you help me?)

Would

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The modal verb "would" is generally used to form the verb tense that would be equivalent to our Conditional or Future Past Tense in Portuguese, as in the conjugations "faria", "iria", "comeria", etc. I would travel a lot if I had more money. (I would travel a lot if I had more money.) Would you go there with me? (Would you go there with me?) Other uses are in the "would like" structure, and also to say something that used to occur frequently in the past, similar to the use of "used to".