I have been doing this for the last 18 months, since our sys admin was terminated. Write stuff down. Find a secure place (or two) on the network to store an Excel spreadsheet with IP addresses, dns names, and credentials for servers, databases, routers, printers. Encryption keys, vendor support websites. Save root, administrator, and sys passswords, and any other admiinistrivia, in some sort of order you can decipher in 3 months at midnight. I use worksheets to identify categories of information.. It's probably more secure to not keep this stuff all in one spreadsheet, but the fact is the document becomes a corporate asset. You can be the keeper of it, and the central answer person--lots of parties need that kind of information. Back it up, encrypt it, whatever. Where I work, only the CIO, two database admins, and the network admin have read permissions on it. Do not print it out, or carry it on a usb stick that can be misplaced. It's an admirable gesture, but probably masochistic to try and store this information in a secure database, because that may run on the server that goes down at midnight when you most need that list. Plus it's freeform-- we keep different columns of data for OS's, servers, cert keys, routers, databases, etc.. It's also nice to have it handy and organized, so you can paste it into vendor inquiries. Saves money and consternation next time you don't have to look up the info ad hoc. It's easy enough to find out the MySql version, but when there are 10+ servers, you will be glad you've got it in one spreadsheet.
Save model numbers, sales staff information, customer contacts, warranty information, service contracts. Also record server software versions. It's easy to remember if you just bought it, but in two years, you will be glad you know It's Oracle 10.1.0.5 and not just 10g. All the big IT suppliers-- Oracle, Microsoft, HP, Dell, NetApp, SAP-- have their own twisted bureaucracies, ticket tracking systems, incident reporting and escalation, and lines of communication. Put as much of that info in the spreadsheet as you can. You can even embed links to support sites in Excel.
Try and figure out which servers talk to each other, which have dependencies and would be affected by an issue with another server. It's good to learn the network topology-- which equipment and services are in which segment and why. Where does the internet come in? Try not to work too late. Don't carry a gun to work. Be nice to the users. That's about all I've got.