How to attach a data file with each customer order?

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To preface this, I am a complete rookie on anything to do with server-side programming.

Vaguely speaking, I built an extension on my Shopify website that lets users adjust the position of images on a canvas they can purchase. I can compile all the positioning data in an object on the client-side, but I have no clue how to send it to the server and retrieve it after a customer makes an order.

I looked through Shopify's storefront API and didn't find anything that helps with attaching data files with customer orders.