I also recommend getting work to pay for some training, especially if you inherited the job as you say. As much as I would like to say to get some Linux + Certification training, those classes really fail at actually teaching you anything other then memorize commands and command options (i.e. the test questions are like "What command will generate a list of all files contained in the "/var" directory and its subdirectories which are executable files and have no owner"? Which knowing the specific command is not nearly as important as knowing how what command might be correct and knowing how to read the "man pages" for the command to get the specific options and syntax for the command. Way too much is spent on direct memorization as opposed to real critical skills and how things work under-the-hood.
A much better class would be the Sun Certified System Administrator I and II classes. Now while these focus on Sun Solaris (Unix operating system), a LOT of the underlying things work very similar for the different linux operating systems (the big exception being that Sun has moved away from "init RC" directories and now using services, in which you set dependencies of a service so that multiple services can be started at once, instead of in the case of the older init RC scripts, one at a time in series).
Anyway, 70-80% of the stuff in the Sun SCSA classes will apply to linux as well. The command might be a little different, but concept is the same. Concepts are going to be your biggest issue right now. You will need to be able to figure out what is going on with the system.
On top of what mgpaulus said, you will want to go document what initialization scripts are running on the system, system run-level, and what type of account authentication method is used for logins. For find out what starts when the system boots up, first look at the "/etc/inittab" file and look for the line that says something like "id:5:initdefault:", where "5" is the runlevel (it might be any value 0 through 6, although if it was 6, you would have massive problems, as the machine would just constantly reboot itself). Once you know the runlevel, you can then find out what starts when the system boots by going to "/etc/rc<x>.d" (replace <x> with your runlevel). Inside that directory you will see a lot of executable scripts (or links). Anything that begins with a "S" will be Started when the system enters that runlevel. Anything with a "K" will be Killed (little more complicated, as the things that are killed are actually from the runlevel above your current runlevel which you don't want running in this particular level.... don't worry, just think of it as stuff that won't be running).
Now that you know what starts when the system starts, you will know better what the system is doing. Next look to see what authentication method is used, look at "/etc/nsswitch.conf" and look at the lines for "passwd, and group", and you may see something like "files [NOTFOUND=return] nis nisplus ldap". Anything before the NOTFOUND part is a possible authentication method, files means local files, nis, means it will look for a NIS domain (you can check to see if you are part of a nis domain by doing a "ypwhich" which will show you the current nis server you are pointing to for the data), nisplus is another method that might be used (although not as common anymore), as well as ldap. For "nisplus" you can try doing "nisdefaults" for getting nisplus information. Unfortunately, I don't know the commands offhand for ldap. It is important to know who can login to the system (for obvious security and data integrity reasons).