The critical information you need to capture are those configurations and settings that are unique to a device or system, anything that makes it different then clicking next, next, next, finish during setup. Specifically you want to get down what it would take to recover the system for next time. ( I know, you just learned that lesson when you rebuilt that server ).
Best practice guidelines for this process are available via any of the frameworks - COBIT, ITIL, ISO 270001. Microsoft Operations Framework.
For a quick documenation project I’d start by diagramming out the infrastructure (firewall, routers, switches, wiring, ups, servers, printers, etc) as it often has the fewest changes over time and will give you the greatest understanding of how the overall architecture has been assembled.
Next I’d map out where the services and applications are located. In this context a ‘service’ is something offered by the IT infrastructure to the organization, anything from that broken share you mentioned through the website, email, the accounting system, etc. Management could care less where DNS comes from, but when it’s broken you need to know where it was and how to get it back.
At some point you’ll be able to add details to the diagrams that aren’t necessary to rebuild the system, but help in operations overall - serial numbers of servers, warranty expiration dates, OS versions (and where the licensing came from), disk space, RAM, video specs… Spiceworks can give you a lot of this information.
You should centralize the documenation if possible, and try to get everyone to help you if you can. Use a revisioning system in the document name (v 1.2.3.4.a) and create a structure so that you can find that specific detail when you need it.
Eventually you’ll be able to take the information you’ve generated and the processes and procedures you follow and combine them into ‘Battle Books’ - or ‘Run Books’ as iandrewmartin called them.