How to allow user's to dynamically add more fields?

I'm creating a reservation form for our field crews to submit on a weekly basis.  The crews range in size from 1 guy to perhaps 15 guys.  So on the form I have "add another" or "I'm finished".  What I would like to happen is if they click on "add another" then it builds below another room reservation.  Can you help?

If I understood you correctly you want to allow your users to dynamically add more rooms. You can achieve that with Configurable list widget. More about configurable list widget you can find here:

https://www.jotform.com/help/282-How-to-Set-Up-the-Configurable-List-Widget 

Inside of this guide you can find how to add widget to your form: https://www.jotform.com/help/252-How-to-Add-a-Widget-to-your-Form 

Here is my demo form: https://form.jotform.com/61745276349970 

Feel free to clone it. 

Other way is to add multiple fields inside of your form, for all 15 rooms and then to use conditional logic to show/hide fields based on user's answers:

https://www.jotform.com/help/316-How-to-Show-or-Hide-Fields-Base-on-User-s-Answer 

Hope this will help. Let us know if you need further assistance.