To quote the game Paranoia: "Trust no one and keep your laser handy."

Backups will be your nearest and dearest friend. If you are new to this, do backups and make sure your backups are good.

One thing you didn't mention is if you're the sole admin or if you're under someone. Learn from them, but learn from outside as well.

My admin story:
I was hired to take care of a HP-UX system. First week I'm there the medical Lab manager asks me if I would know what could cause all medical systems to be cut off from the HP at 1am every night. If the lab hadn't finished processing by 1am, they would have to start over.
I immediately think that sounds scheduled and notice backups start at 1am. Look in the script and wow, there's a few kills involved.
I move the start time to 3 am after checking some other dependencies. This takes 15 minutes at around 6pm.
I shoot an email to my manager who had gone home at 5pm and talk to the lab manager. She's thankful and when I get in the next morning I find a nice note on my desk from the lab people.
I then get chewed out by my manager. He's really pissed, but I don't get a real reason why. He goes away after I go over what I did showing him why it works. (All of which was in my email)
Later that day I find out he had been telling the lab for the last three months that there was no way to fix it. I had cost him major points. He worked hard to fire me for the next year.
So find out what the environment is like as well as the systems.