There are two levels of customization:
Custom CSS
You can customize the modal just purely using CSS. Here’s an example of the standard exit modal compared to a version of it customized using CSS.
Custom HTML / CSS
If you would like to fully customize the HTML in addition to the CSS, you can do so by dropping the HTML in the Magento admin using the Additional HTML field.
Use the following HTML as a template (please login for the source). It’s important that all of the id and class attributes stay the same with your custom markup in order for success / error message states to function properly.