Hey Miquel,
Thing is that the ordering process is divided into several steps.
First, you create a cart item with the Cart Item Creation API. On this step, you submit a 3D model file or an ID of the previously uploaded model, material and finish, quantity, scale factor, etc. In response, you receive a cart item ID.
Then, you need to create a cart and fill it with cart items. This is done with the Cart Creation API. You provide the cart item ID, shipping and billing addresses. In response, you receive a cart ID and a list of available shipping services.
Finally, you order the created cart using the Cart Checkout API. You specify the cart ID and the shipping service. In response, you receive an order ID and can use it later on to check the order status with the Order Status API.
Order payment is not part of the API and is done offline.
Does this explain the workflow?