There are three main API calls to let you list and connect to services.
/user/login is used with your remot3.it account credentials and Developer API Key to get a login token which is required for all other API calls.
/device/list/all is used to list all services registered to your account.
/device/connect is used to make a proxy connection to one of your services.
Click on top link the "API Reference" to start exploring the details.