Hi Rosie
What is the main ambition of the project? Is it to replace the system or upgrade it for example?
Knowing what the main reason for doing this is will enable us to understand what you are trying to achieve. So, does your documentation need to be more technically slanted or more process driven?
My first steps would be:
1. Get full access to the system (if you haven't already). That way you can document screens and User journeys throughout the system. Make sure it is full access though, not just a Customer's access.
2. Find out who is responsible for the code maintenance of the system. Somewhere there is a developer who either currently does, or previously had written code for the system. Speak to them as they will probably be able to give you some technical data about the system.
3. Does your company have Technical Architects? If they do, then they will also be good to speak to as they will be able to advise you how the system fits in with your technology stack - what systems are a dependency to it, and those that depend on it themselves? Note, speaking to the Technical Architect will give you different information from the Developer. The Developer should be able to tell you about the workings of the system you need to document - what it's failings are, how much time and effort it needs to bring it up to scratch, known issues etc.
4. Can you also find out who was previously the Product Owner for that system? If you can (and your company has them) then you may be able to find out what plans were considered (and why they weren't implemented) for the system.