If the standard documents like System Requirement Specification or Feature Description Document are not available, then QAs may have to rely on the following references, if available.
Screenshots
A previous version of the application
Wireframes
Another reliable way is to have discussions with the developer and the business analyst. It helps in solving the doubts, and it opens a channel for bringing clarity on the requirements. Also, the emails exchanged could be useful as a testing reference.
Smoke testing is yet another option that would help verify the main functionality of the application. It would reveal some very basic bugs in the application. If none of these work, then we can just test the application from our previous experiences.