Hello.

Say I have an image, and I want a certain part of it to be clickable, how do I do that?

http://www.w3.org/TR/REC-html40/struct/objects.html#h-13.6

You want to read about image maps. I would avoid this practice as much as possible too. You can find major accessibility issues when using image maps. Dreamweaver and most WYSIWYG editors have an easy tool for creating image maps also.