How to add an export function to a custom Option Theme Page

I’m creating a new WordPress template and I have a question:
I’ve added a custom Option Page to my new template (you can see what I’m doing Here and Here) but now I would like to add a new function.
Do you know Si Contact Form? In this plugin the end user can download a backup of all the settings and Upload it on a different website.
I would like to be able to add the same function into my new option page.
I know how to backup my settings logging to phpMyAdmin but sometimes end-user can’t login to phpMyAdmin or simply it’s better that he/she doesn’t login to phpMyAdmin :-).
Have you got any solution to this?
Actually all my custom functions are named:
‘appaqua__zona1c’;’appaqua__zona1x’ and so on… my theme shortname is appaqua.
Please by kind with me, I’m not a professional programmer and I’m really sorry if I used wrong words to explain what I need.
Thank you very much to all!