These auxiliary verbs are best understood together:

1. Will / would refer to a result, consequence or act that comes after now (or the time in question: the focus time);
2. Can / could talk about ability;
3. May / might mean that something is possible or has a chance of happening.

They divide in meaning in two ways. Look at the table:

The UNREAL side is hypothetical: what you imagine. Using would / could / might often implies an IF.

Examples:

1. I would visit India (if I were you).
2. You could visit India (if you wanted to).
3. We might go to India (if we can afford it and feel like it).

The REAL side is sure: you know it is the case. When you use will / can / may you are certain.

Examples:

1. I will go to India (not France, not Peru... etc).
2. I can go to Japan (I got a tourist visa).
3. I may go to Korea (but I haven't got a visa yet).

Would / could / might are conditional forms of will / can / may. Conditionals require something else to happen first for them to be true. Consider this example: If I had a million dollars, I would quite my job. For me to be able to quit, I need a million dollars first. Once we are in this conditional world, then using will / can / may is a switch back to reality. Be careful when you do.

Another way to think of the different aspects of these words is to look at them as sets. What you could do is the biggest, limited only by your imagination. You could do anything you want. What you might do is more limited. What you would do is the smallest range of possibilities.

You can apply the same logic to the can / may / will set. You can do lots of things, you may do some, but there are fewer things you will do.

Try these differences out with your writing and test your understanding. Also have a look at this page about may and might to help you see the difference.