I first thought on this is "The people responsible for design and writing the software are also responsible for documenting it, not the people responsible for supporting it".
You, as the DBA, simply see a bunch of tables and columns which may have not business meaning or context. Reverse engineering these things into an ERD may help you a bit but it still doesn't give you enough.
The developers, now they really should have a complete understanding of what they just did and they are the people who should be responsible for production of the ERDs. You as the DBA, may have a responsibility to ensure that all the required design documents have been produced before permitting software to be promoted into production. When I was a DBA in one of my past lives, I flatly refused to release changes into production if they weren't up to scratch.
As for tools, that you could use, there are many out there. I use "Enterprise Architect" from Sparx Systems. It does a fantastic job and at about $US240 a seat, it is pretty hard to beat.