The Manager.io API works via JSON. To see API, intuitive, use http://www.youraddress.com:Port/api (e.g www.abc.com:81/api ) login with your admin details and you click through json feeds (Note: You can only do API with server edition)
You can create sales quotes, purchase orders, etc using api GET, PUT, POST and DELETE
What language do you use? Here are examples in php