Form Validation for Custom Plugin

I am developing a custom plugin with an admin menu containing various screens with forms for adding/editing information. These screens are similar in appearance to the built in “Categories” page with a list of items and a form to add a new one.

I want to add some javascript validation to these forms using the built in functionality, but I can’t find any information on how to do it.

Can anyone suggest a good example or tutorial?

Thanks.