"I can do this" and "I am able to do this" has the same meaning. But the second sentence is more formal. The first one is a bit informal.

But if you want to add helping verbs (also known as auxiliary verbs) you should use "be able to". Would and might are helping verbs. You cannot use "can" with them.

Example: 

I would be able to do this, if I had the right material.

or

I might be able to do it if you were nicer to me.

Hope this helps! :D