Modals are different from normal verbs:

1: They don't use an 's' for the third person singular.
2: They make questions by inversion ('she can go' becomes 'can she go?').
3: They are followed directly by the infinitive of another verb (without 'to').

First, they can be used when we want to say how sure we are that something happened / is happening / will happen. We often call these 'modals of deduction' or 'speculation' or 'certainty' or 'probability'.

For example:

It's snowing, so it must be very cold outside.
I don't know where John is. He could have missed the train.
This bill can't be right. £200 for two cups of coffee!
Click here to find out more about probability. 

We use 'can' and 'could' to talk about a skill or ability.

For example:She can speak six languages.
My grandfather could play golf very well.
I can't drive.
Click here to find out more about ability.Obligation and Advice
We can use verbs such as 'must' or 'should' to say when something is necessary or unnecessary, or to give advice.

For example:Children must do their homework.
We have to wear a uniform at work.
You should stop smoking.
Click here to find out more about obligationPermission
We can use verbs such as 'can', 'could' and 'may' to ask for and give permission. We also use modal verbs to say something is not allowed.

For example:Could I leave early today, please?
You may not use the car tonight.
Can we swim in the lake?
We can use 'will' and 'would' to talk about habits or things we usually do, or did in the past. 

For example:When I lived in Italy, we would often eat in the restaurant next to my flat.
John will always be late!
Past modals
The past modals 'could have + past participle', 'should have + past participle' and 'would have + past participle' can be confusing. I explain about them here.