In the present:
“Can” and “able to” are the same in the present tense:
Yes, I can take on this project.
Yes, I‘m able to take on this project.
The negative forms are can’t and am not / is not / are not able to.
In the past:
We use “could/couldn’t” or “was/wasn’t able to.”
In general, both are used in the negative form:
I wasn’t able to finish all my homework yesterday.
I couldn’t finish all my homework yesterday.
But in the positive form, “was able to” is more common than “could”:
I was able to leave work a little early yesterday.
Don’t say didn’t can in the past – it doesn’t exist, and it’s a common error in English!
In the future:
In the future, there is only one form: “will be able to”:
I have some free time tomorrow, so I‘ll be able to work on this project.
Sorry, I won’t be able to go to the party on Thursday. I have school the next day.
Don’t say “will can” or “won’t can” – it’s another common error in English!
When asking someone to do something:
When you are asking someone to do something, use “could” (more formal) or “can” (more informal):
Could you bring me a glass of water, please?
Can you bring me a glass of water, please?
When asking about someone’s abilities:
In this case, you can use either CAN or ABLE TO:
Can you run a mile in less than 10 minutes?
Are you able to run a mile in less than 10 minutes?
Can is probably more common in spoken English, simply because it’s shorter.