Orders made in your OAL app are made directly with your Square account. You'll be able to see any orders made on your OAL app, directly on Square admin and proceed by Square using your OAuth token.
Orders work exactly the same as they do in Square, except with added functionality of pickup options. Pickup options allow you to control how your customers receive their order. View how to create a pickup option to understand pickup options. You'll set pickup options, based on the location their ordering from, for your customers to pick from during their checkout process.
Your customer will add the items they wish to order to their cart. Then when they are ready to complete and pay they will go to checkout and provide a payment option and pickup option. There will be a moment for your customer to review their order before paying. Once ready they click PAY to pay, from here depending on your order settings the order will automatically be accepted and have the payment completed. If not, you'll be required to either accept the order to complete the payment or deny it thus invalidating the payment capture from be proceeded and releasing the funds to your customer.
Currently orders do not adjust your Square inventory.