It sounds confusing, but is quite simple. I have a
square div, and using css I have four circles
replacing the corners of the of the divs border. I
want the user to be able to click on one of the
corner circles changing the curser image and
calling the Javascript onclick event. How do I did

Do you use border images or border-radius?

Well, than you can just assign onclick events to those images. PPK talks a lot about that here (traditional) and here (W3C and MS).

Sorry, I'm getting little confused ;)

I have a div with a black border...

<div style="border: 2px solid black;">&nbsp;</div>

I want the bottom right corner to have a small circle instead of the border. How can I do that? Also, when the user clicks the bottom right corner I want an onclick event to take place. So can you transform that code above to what I'm looking for?

Position an image that has that on that place?

As @twiss says, position the image on this place and attach the event to the image. Just simple CSS.