In a nutshell, POD is integrated with your Shopify account using any of these third party apps from the Shopify App Store; Your designs are created directly within the apps.
Once a design is complete, the app will turn it into a Product within your Shopify admin. The product information will be directly linked to the app of the POD supplier it is from. So when a customer makes a purchase, the order coming through your online store will also go through to the respective POD supplier. Each supplier will make and ship the item(s) separately to your customer. Does that make sense?
Here are a few resources containing more information that you may find helpful to get started:
What type of products are you going to be selling through print on demand? Do you already have some particular POD companies in mind that you’d like to work with?