Can and could, will and would
Champok from Bangladesh writes:
  I often get confused regarding the uses of will and would and can and could. Would you please help to clarify them for me?
Roger Woodham replies:
Can and could are used in a variety of different ways for different purposes. We can use them to talk about ability and possibility, to make requests and to ask for permission.
can and could: to express ability
Here the distinction of can for present scenarios and could for past situations is preserved:
He could read by the time he was four years old and now he can speak six languages fluently.

I couldn't find my Tom Jones CD when I was looking for it the other day, but now I can see that you have it.
can and could / will and would: to make requests
When making requests, can and could are both used to refer to present and future situations. When we are asking something of others, will and would are also commonly used alternatives. Compare the following:
Could I have another cup of tea, please?
Can I have some more tea, please?

Could you pick Lauren up from school for me this afternoon, please?
Can you pick up Lauren from school for this afternoon, please?
Would you collect Lauren from school for me this afternoon, please?
Will you fetch Lauren from school for me this afternoon, please?
Note from the above examples that could and would sound marginally more polite than can and will.

Note that if we are talking about ability to do something, rather than making a request, it will be necessary to use will be able to talk about future ability:
Will you be able to pick Lauren up from school this afternoon by any chance?
Note also that if we want to sound particularly polite when making a request of others, we can use the would you mind + verb-ing construction:
Would you mind picking Lauren up from school? ~ No, I don't mind. It's no trouble.
We can also use will to express the speaker's willingness or intention to do things:
We haven't got any paper for the photocopier. ~ I値l get some for you.
Can you lend me fifty pounds for the weekend? I値l pay you back on Monday.
can and could: to ask for and give permission
Can is more commonly used than could in these contexts. May is a further alternative:
Can / May I help you with that? ~ Yes, you can.
Can / May I carry that for you? ~ Yes, you may.
Can I enter the room while the recording is in progress? ~ No, you may not.
Can I listen to it afterwards? ~ No, you can't.
Note in the example above that we cannot use couldn't when refusing permission.
reported speech
In reported speech, would and could or would be able are used after reporting verbs in the past tense where will and can are used in direct speech. This is because there is a difference in time, place and speaker:
I値l tell Mary about the meeting you've arranged for next Saturday.
He said he would tell Mary about the meeting tonight, but she's not here yet.

I can look after Jenny if you池e busy.
He said he would be able to look after Jenny if I was busy.
However, would and could do not change in reported speech, if they are already present in direct speech:
It would be great if you could come to Manchester too.
He thought it would be great if we could go to Manchester as well.
conditional structures and future situations
To talk about things that will probably not happen, we use a past tense in the if-clause and would, or sometimes could, in the main clause. Compare examples above and below:
If I knew where she was living now, I would tell you. But I don't know.
To talk about things that may happen in the real future, we use a present tense in the if-clause and will, or sometimes can, in the main clause:
I値l try and repair your bike tomorrow, if I have enough time.
I値l try to mend your bike tomorrow, if I can find enough time.