[Trerro]

If I've given you the admin login and op rights, there are a few things you can do with it.

Backing up the world
1. In game, type /save-all.
2. Connect to the server IP with a secure FTP client. I use WinSCP personally, it's a good free one.
3. Go to the Minecraft directory.
4. Copy the entire contents of the World directory.
5. Zip it, and name the zip file with the current date.
6. Copy the zip file to Backups, and also save a local copy.

Op Commands
http://www.minecraftwiki.net/wiki/SMP_Server_commands - This lists all of them.
If you ban someone, please let me know who and why.
Please do not use the give command unless there's a very good reason for it, such as a server crash causing someone to lose the loot from a cave run.

Directly adminning the server
If you'd like to know how to start and stop the server, ask, and I'll explain what to do. It involves doing everything a from a remote terminal.

[Sonya the fox]

Is there a way to alter how many lines of log the screen will keep?  I find we get maybe a partial idea of what may have been going on when it throws up 'Killed', a longer log length might help us some on figuring out what causes the problem other than the fact 'the server couldn't keep up'.

[Trerro]

You can view the actual server log file, which seems to either go back 4 weeks or 500k of entries, it's hard to tell what the cutoff is as it's close to both atm.

Connect via SSH, and type cd minecraft, then nano server.log. To jump to a date, hit control-w, then type in the date in the format the log file uses, I think it's yyyy-mm.dd.

If you'd rather load it in a text editor you're more familiar with (and have full mouse controls), log into the server via secure FTP (WinSCP is a decent free client for that), copy the log file to your own machine, then load it with whatever. Notepad will blob everything together because it doesn't know how to read a linux-style text file, but any good text editor can read it fine. Textpad (also free) is the one I personally use for this sort of thing.