To authenticate against the API, you need to provide your API key in the request header with apikey <API-KEY>. The following is an example request to fetch all recent submissions from your instance, note that you need to prefix your instance name with api-.

curl -H 'Authorization: apikey <API-KEY>' \
    'https://api-<YOUR-INSTANCE>.analysis.threatray.com/v1/submissions'

You can find your API key in the settings menu. It carries all your privileges, so keep it secure and don't share it with anyone.