The Reservation API has a base URL to which extra parameters are added to have it perform specific reservation functions. To obtain the base URL for a particular segment, go to your TROPHiT dashboard => User Segments, select Settings of the desired segment and get the Reservation API URL:
The format of the base URL for any reservation operation is:
https://api.trophit.com/segment/service/?app_key=<app API key>&id=<segment id>&...operation-specific parameters...
Note: app API key is not your account's API key, and is provided by TROPHiT for some app-specific API calls.
Check out the documentation for specific operations.