chmod - give/take rights away from files. The numbers you see in the how-to's is a little complicated. It has to do with the rights you are assigning the file or folder. http://wiki.linuxquestions.org/wiki/Chmod for further reading.
cat - look at, modify, or combine a file. You can also copy files with this command by "reading" it to another file instead of to the screen.
cd - change from one directory to another
cp - Copy a file from one location to another
dd - copies exact locations to other locations. Can be an entire drive, a folder, etc.
dd if= of=. uses an input file and an output file.
exit - exits the shell you are in. When you type su you start up a shell.
ls - lists all files with in a directory try ls - l too.
mv - Move a file from one location to another. At the same time you can rename a file.
su - Substitute User. We type this to switch to the root user. You need to type this command first to do a lot of the other commands.
tar - creates taped archives. Compresses files like winzip, 7zip, winrar and others tar /? for details.
rm - followed by a file name with delete the file sync - synchronizes any data on disk with data in memory. We type this before rebooting to ensure we've got all data written
Other commands of interest:
df - how much free disk space. In linux you can add a switch "df -h" but the "-h" does nothing for me on Android. top - like task manager, it displays running processes. in Linux the q key quits. On Android I don't know how to make it quit other than closing the app. uptime - displays how long it has been since you last rebooted the system.
busybox - a tool that combines many linux commands into a single compact file. Typing this displays all the commands at your disposal.
busybox df - a much easier to read display of free diskspace. This display shows how full (use%) each file system is.