First, select “Custom” as your theme on the Settings screen. Then copy one of theme-standard.css or theme-basic.css to /wp-content/themes/your_theme/petition.css. This will be a template for your new styles. Now you can edit petition.css and unless you change themes, your custom styles will not be modified by the plugin.
Custom styles can also be created for the widget and signaturelists by creating petition-widget.css and/or petition-signaturelist.css to your theme directory just as you did with the petition CSS and you also change the CSS setting these items to “None”.
Of course, you can always use the WordPress custom CSS option, however if you change themes they are lost.