Using Ajax to submit a search form

I have a customized search form that's currently processed on a different page. I'd love to be able to use Ajax to process the form on the same page.

Could you please tell me how to do this -- or point to a tutorial on it? (My search form searches content and filters based on different criteria. It's not the simple get_search_form.)

The form and processing are all taken care of. I just want to know how to use Ajax to submit the form to the same page and have it be processed by my php code and displayed.

Thank you!