Well, this is a usual scenario that every testing team faces.
First thing first, get in touch with Business Analysts and other stack holders and understand the product domain. Once you start understanding product domain, you will be able to ask questions and get to know the system much better. Ask questions until you have the complete idea of an application. Now once you have the fair idea of an application, start writing manual test cases and get it validated from the BA or stack holders.
If you are following agile, definitely your scrum master will have sprint planning done and will have user stories in hand. Based on the user stories you can write manual test cases.
As a manual tester, understanding the domain in which application is developed and working closely with the dev team is very critical if you do not have the requirements document.
