First off, I don't want to insult your intelligence so tell me if I'm being too simplistic, but it sounds like you don't have a good handle on how things work. Perhaps having a better understanding of the bigger picture might help you. (and you are totally right, better documentation, although that is a community effort and a work in progress).
First off, in essence having TikiWiki installed on your computer is absolutely no different to having it on a webserver, accessible through the Internet. The only difference being that YOUR computer IS the webserver (AND will also be used as the client, when you access TikiWiki through your browser) and that nobody else on the Internet will be able to see your computer (unless you configure it otherwise).
The TikiWiki application, in an oversimplification is really just a collection of web pages that reference a database (there is of course more to it than that, but that is what happens at the most basic level). In particular the web pages are PHP pages, which is simply server side (remember your computer is the server AND the client) programming language that interacts with the web server.
So to recap, to use TikiWiki we need a webserver (Typically Apache) to send web pages to the browser. PHP to understand the code and tell the webserver what pages need to be sent to the browser, and what information needs to be stored or retrieved from the database and MySQL, the database that stores all the information that can then be accessed by PHP. This is where the term "WAMP" comes in because it typically stands for Windows Apache (web server) MySQL PHP (I say typically because now you can find "LAMP", which is the same thing but for the Linux operating system and in the case of "XAMPP", this runs Windows, Linux and other operating systems, so it is cross-platform, hence the 'X'.)
Now to address your question about where the Tiki files go, as I mentioned previously, in the WAMP installation that you are using there must be installed files somewhere on your PC. Typically, within the installation folder for the WAMP you will find a subfolder which is designated as the "root" for all web pages, so that any web pages you place in that "root" folder, will be accessible when you browse to http://127.0.0.1/
So you might have something like this:
(I'm guessing here, it's different for different WAMP packages)
You should unzip your Tiki files to that path given above. If you want to, you can create a sub folder in htdocs as in:
What this means is that when you browse your Tiki in your browser instead of using just http://127.0.0.1 you will need to go to ''http://127.0.0.1/tikiwiki/
Once you've unzipped your files simply browse to the appropriate folder in your browser but add tiki-install.php to the end of the localhost address as in:
You should then be guided on what to do next but it essentially involves telling Tiki the database username and password, and then administerting your Tiki (which is where the real fun begins... turning features on or off, setting up the look and feel etc etc.)
As a small aside you can usually use http://localhost in place of the IP address (http://127.0.0.1). That IP address or the term "localhost" simply tells you browser to look on your computer rather than going out to the Internet.
And I urge anyone else in the community to correct me if I have got something wrong.
As for Latex, I've not used that with Tiki so I defer to somebody else on that issue, but I would say that you probably want to check the features first and get a feel for the application before you start adding other "mods" (custom modifications).