First, please understand that asking questions is often the only way we get to learn what it is we need to ask about when we start something new. No question is really stupid - do not ever think that. Look at some of the questions I asked here first, over the last year or two, they are essentially the same questions.. And there are a lot more, believe me.
Assuming you are using Windows, download and install MikTex that is a good place to start for Windows users. This is a real TeX package, creating PDFs which is where the image came from. It is easy to learn and use and you may find it a better tool than the native Tex Notation Filter, but it will mean importing PDFs, or screen grabs, into Moodle. If you get adventurous, LiveTex is an alternative, but it is huge,
Moodle uses a version of TeX based on Mimetex, and is not a complete Tex tool, having some rather large flaws, but it mostly works and provides an element of Tex notation for use inside the Moodle environment and is infinitely better than nothing at all.
Mauno has been working on developing a standard for using a number of other TeX tools, which is really exciting and looks great, but it is only going to be for Moodle 2.0. In the mean time, Marc Grober has been praising AsciiMath as a tool for Moodle - and that is very nice too.
Good luck with it. Work time..