I am brand new to Linux - taking a class on it actually. I am having a hard time finding a good resource to define things for me. I have bought "Linux in a Nutshell," and that is good for looking up commands that I already know of and am wanting to use. But does anyone know of a good resource where I can search for things such as "how to make a user an administrator of a group" and such? I am trying to find a book or a website for this, rather than googling everything I come across.

Another thing I am having trouble finding is a place that defines all of the necessary partitions - meaning what they do and what they are used for. Examples being /usr/local/, SWAP, /bin/, and things like that.

I apologize for the very very VERY newbie-ness, I'd be very thankful for any pointers.

The Linux Documentation Project is a good place to start. Look for Bash Guide for Beginners, and the Filesystem Hierarchy standard..
Also, check out the O'Reilly website. The have the Safari service + even some free books.

One nitpick; The things you listed are all typical directories--not partitions. All Linux directories--except SWAP--can be in one partition.