But, there are ALWAYS requirements - even if they are not formally documented. They may take some time to discover and list, but they exist.
First, look for general requirements and work to document them. Some of these requirements come from previous versions of the application, some come from generally accepted usage.
Then, interview the project manager or developers and find out what they intend to do with this release. Document the intentions and use them as requirements.
Sometimes, writing all of this up as assumptions can go a long way toward gaining a consensus as to the "real requirements" you can use to test against.
Once the system is at all testable, do some exploratory testing. As you find "undocumented features", add them to the list of topics to be discussed.
Find out if the product is internally consistent. (This is an area I find to be very useful) Even if I know nothing at all about a product, I assume it must be consistent within itself, and within the environment in which it must operate.
Look for external standards within which the product must operate. If it is a tax or accounting program - tax law must prevail and generally accepted accounting principles must apply.
see: There are ALWAYS requirements