Collect data during enrollment

Summary

Is there a way to collect data from a user during enrollment?

Content

This morning we received a request to collect user entered data during self-enrollment or Manager enrollment. I know that you can add custom roster fields that allow for data entry, but have not explored. I have reviewed portions of the enrollment and roster instructions in help.learn.com and I understand that there is a path for allowing admins/managers to add this information. But 

Does anyone have any further information on:

• User Experience for self-enrollment and Manager enrollment?
• Permissions to be set?