I believe you need to clarify the basic concepts before trying to work with any software. If you find this difficult to do by yourself, consider getting training - any CAT software is a professional tool, and unless you get trained properly, the investment will be lost.
As a first step, check the various articles in the Article Knowledgebase (use the link provided above - select Technology - CAT tools).
But I can get as far as the TRADOS folder, but then only find "TRADOS" and "T65_FL". I have gone into each of those and all of their subfolders and directories and cannot find anything resembling the samples described.
In your initial posting, you indicated that you're using Trados 7.5 - why do you have a "T65FL" folder? Did you install this yourself?
I have tried simply opening my own Word document, but I am always told by Word that "No Translation Unit seems to be Open."
Did you get this when opening a document? Did you get this message in Word, or in Workbench?
You can, of course, use your own document to follow the workflows; the sample TM is provided to help you get started, but you need a matching document to work with this.
The Trados File Formats Reference Guide (installed with the software, under Documentation in the program group) is also helpful to gain an overview of the workflows.
I have looked through the help sections and the tutorial and have followed all of the various steps described to configure Workbench to Word (configuring Term REcognition Options, Term Recognition is checked, I went through all the steps regarding "Templates and Add-Ins" in Word).
If you're confused about Workbench, I would suggest to start without term recognition, and to activate that at a later stage.
I am also wondering how this will work with other documents - the Sample is just there to teach me how to use this, but I don't find any documentation on how to work with documents that I simply have on my computer and would like to translate. Do I need to create a new translation memory each time, and if so, how do I go about that?