This article is meant to serve as a collection of ideas to help with your integration design. It will grow over time. As always, please reach out to us if you have any questions.
API
Please see http://help.vinespring.com/vinespring-3/storefront/v3-vinespring-api-introduction and https://vinespring.docs.apiary.io.
Carts
You can build a custom storefront elsewhere, create a cart using the API, and when your customer is ready to checkout, your custom storefront can redirect them to your VineSpring hosted storefront using https://<your VS hosted storefront>/#/auth/<customer's auth token>/cart%2F<cart id>.
Webhooks
Please see http://help.vinespring.com/vinespring-3/storefront/v3-webhooks.