If I create a new edit form (separate to the default one), how can my users invoke it? Can I create a field on my page that links to it?
Page versions cannot be linked to. Rather, the system is designed to allow you to assign page versions based on Role and/or User (user-specific assignment will override role-base page assignment).
To do this for Roles go to Setup -> Administration Setup -> Roles and click on the "Pages" link next to any Role. Here you can assign page versions per object for that role.
You can do the same for users by going to Users -> click on a user, then select the "Assign Pages" option from the "More Actions..." drop-down
Hope this helps,
Matt