The product barcodes will be generated based on what you have in the "Barcodes" field on your Variants in the Shopify admin.
If you haven't set them up yet, you can do it directly from your products information, as illustrated in the screenshot below:
Note: The barcodes won't show up until after 4 hours after configured. The app imports all barcodes on a 4 hour cycle, so they'll show up automatically on new orders as soon as the app has detected them.
Once you have them all set up, you can include barcodes in your templates by doing the following:
Login to OrderlyPrint (Shopify admin -> Apps)
Go the Settings -> Document design page
Go into the Options and formats section of the editor
Scroll all the way to the bottom to the "BARCODES" section, and enable the check-mark for the barcode options you want.
That's it! If the product barcodes were just added or updated, old orders won't have the product barcode because Shopify will not update old orders when you make this type of change, but new orders will certainly show them.