I was just given an I Mac with Linux. The system boots up, but it wants a user name to get in. I don't have a clue as to what this is. Is there any way to by-pass this, and use this machine ?

Welcome to LQ!

You probably know with Linux (UNIX) there are at least two accounts in OS. User(s) accounts are for using the computer and root account is for maintenance. In your case you need root access so you can create a new user account for yourself. This can be achieved in at least two ways.
First, you can boot up in single user mode, in this mode you will be given root access without password. The exact procedure is distro-specific, you need to read your distro's documentation how to accomplish this.
Second, you can boot up with install CD or some LiveCD what works on your hardware and chroot.

Thanks for responding, Emerson. I have, unfortunately, no experience with Linux at all. Can you tell me where to go to get the info I need ? I've been using Win2K, but I've been wanting to try Linux. I've read all kinds of good things about it, and I'm tired of Microbill tell me what I can and can't do

You need to know what distribution you are using. Then go to their home site and look for documentation. You may want to download the install disk, this disk can also be used for maintenance and repair.

Great sources for learning Linux:
Rute tutorial
The Linux Documentation Project
http://www.google.com/linux
Searching these forums is very useful too, most questions newcomers may have are answered here already.
And, as I mentioned above, your distro's home page and documentation.

Good luck.