Our API follows the REST principles as much as we can.
Every request must include the user token and the account API key.
curl -d 'token=XXXXXXXXXXXX&api_key=XXXXXX' -G https://url
The token and the API key can be found by logging into your Trigger account, clicking on your profile picture (upper-right corner), clicking on "My Settings" link and scrolling to the bottom part of the page.
Be sure to set both 'token' and 'api_key' to be able to retrieve any data. Example with cURL:
curl -d 'token=XXXXXXXXXXXX&api_key=XXXXXX&format=xml' -G https://www.triggerapp.com/api/v1/me
Format can be specified as a parameter or in the url as /XXX.json or /XXX.xml