Hello @sjlabar,
To add new custom fields to registration form you can use BuddyPress plugin and its eXtended Profiles (Membership has add-on for the BuddyPress). Also you will need to switch to BuddyPress registration form:
If you would like to use profile fields that are in WordPress default profile field then that add-on is available only in Membership 2 Pro.
Another solution is to use plugin like Gravity Forms (or any plugin that can make registration form) to create registration and then add this line to functions.php of your theme so Membership will know that other plugin is used
add_filter('ms_frontend_handle_registration', '__return_false');
kind regards,
Kasia