How do you use 'can' and 'could' correctly?

A PhraseMix reader asked this:

Please tell me which verbs can be used with "could"? In the present past as well as future...?

"Can" and "Could" are tricky because you can use them for a few different purposes, and the rules are different for each version.

"Can" and "Could" for ability

You can use "can" to talk about things that someone is able to do:

I can speak Spanish and French, too!

In the past, "could" is actually a little tricky. Sometimes we say "could" (for abilities that were long-lasting) and sometimes we say "was able to":

I could already read by the time I entered kindergarten.

I was able to get us a couple of free tickets.

When you're talking about the future, you have to use "be able to":

Do you think you'll be able to remember all of that for the test?

"Could", "can't", and "couldn't" for belief or possibility

You can use "could" to talk about something that might be true:

A: Why's there so much traffic?

B: I don't know. It could be because of the baseball game getting out.

"Could" in this cind of situation can be replaced by "might".

You shouldn't use "can" to discuss possibilities. 

But you can use both "can't" and "couldn't" to talk about something that you don't believe is true:

He can't be 18 years old already! Last time I saw him, he was still in elementary school.

This couldn't possibly be the last one, could it?

"Can" for making offers

You can offer to help someone with "Can"

Can I help you with those bags?

It's possible that some English speakers might use "could' in this situation, but usually not.

"Can" for permission

English speakers often use "can" to ask for something:

Can I leave a little early today?

This is a casual way to ask for things. A more formal word to replace "can" is "may":

May I borrow your stapler?

You can also tell someone that they don't have permission for something:

You can't go in there.

"Can" and "could" for asking for making requests

Ask people for something with "can":

Can I get a bacon cheeseurger with pickles and lettuce?

Can you email that to me?

You can make the same requests with "could", which is more formal:

Could I get a bacon cheeseurger with pickles and lettuce?

Could you email that to me? 

There are a lot of other little complications, but to learn to use "can" and "could" correctly, you'll need to get a lot of practice with reading, writing, hearing, and speaking natural English.