When do I use "can" or "could"?

When should I use can? When should I use could?
What is right under what context?

Since your name seems Indian, I'll also mention a common Indian-English idiosyncrasy that may clear up matters for you. There is a tendency in Indian speech to use "could" for "can", and "would" for "will". This is wrong (or, to avoid being prescriptive, certainly at variance with other varieties of English, and non-standard even in India). Properly, "could" (subjunctive) is used to express possibility, things that may or may not happen, may or may not be done, etc. (to ask polite questions, for instance) — or in the past tense. If you're using it in the same sense as "can" (for a straightforward expression of ability), you're probably using it incorrectly.

For instance:

• We could go (if we like / but we won't / etc.), but
  We can go (= We are capable of going / It is possible for us to go)

• They could see us from the tower (if they were not blind / yesterday), but
  They can see us from the tower (=they are capable of seeing us, now)

• Wrong: The speaker would be coming tomorrow.
  Correct: The speaker will be coming tomorrow. (The progressive is fairly common in IE, but even more natural to just say "The speaker will come tomorrow.")

To keep it simple, I answer you without complex grammatical terminology. There are five possible situations of using can.

1. Ability
In the first situation, we use can with a meaning of ability. For example, "I think I can lift the box" means that the speaker thinks that she/he is able to lift the box. The past tense form of the sentence is "I thought I could lift the box".

2. Permission
In the second, we use can with the meaning of permission. Undoubtedly, all permissions are questions. Example: "Hey Jim, can I use your PC for awhile?". Use could for more polite forms. Example: "Could you please allow me speak?".

3. Request
In the third case, we use it as a form of request. Example: "Can you please write it for me?". Use could for more polite form. Example: "Could you lend me $100?".

4. Possibility
Sometimes, can is also used to mark a possibility. Example: "Using mobile phones while driving can cause accidents.". Use could if the possibility is uncertain. Example: "He could arrive later."

5. Offer
When offering help to someone, use can. Example: "Can I open the bottle for you?". Could is unusual, formal, and archaic here.

Could is used in two more ways where can isn't normal.

1. To make suggestions
Example: "We could go out for awhile, if you like."

2. To express, forcefully, what someone must do
Example: "You could speak up!"

I hope that this answer could help you a lot! :)

"Could" is the subjunctive form of "can." That means you use it to express possibilities and the like. "I could go to the movies, but I might just stay home."

When "could" is used as the past-tense of "can," you're talking about something you used to be able to do, but can't anymore, so whatever action you're speaking of is hypothetical. "I could have gone to the movies, but I decided to stay home," or "I could mow the lawn before my back injury." (Really that second sentence should say "I could have mown...," but a lot of people don't bother.)

The subjunctive is also used when talking about emotions, wishes, judgments, and such like. Honestly, Wikipedia is probably better at explaining the subjunctive than I.

Good luck!

The difference is one of mood and tense. kitukwfyer hits all the right notes here.

The subjunctive also helps differentiate the forms in questions. Compare:

• Could you run (please)?
• Can you run?

Could lends politeness to a question in a request of someone. I’d more likely say, “could you help me”, than “can you help me?”.