If I understand your question correctly, you want to know what is the minimal set of tools you need to be familiar with in order to use LaTeX to write technical documents. I'll try to summarize these here, and how they work together. I'll keep this answer fairly schematic, and point you to many other questions on the site which will provide some more detailed information.
Main components for using TeX
There are three main components to using LaTeX on any computer: you need a TeX Distribution, a text editor, and a PDF previewer. Within the TeX distribution are numerous engines which are the programs that actually process your LaTeX source and turn it into PDF. Schematically this can be viewed in the following way:

Editors
Although any plain text editor can be used to edit TeX source, most people use an editor that has an integrated system for interfacing with a TeX distribution so that you can compile your document from within the editor. Many of the popular editors also incorporate a previewer into them, so although the previewer part of the diagram above is logically separate from the editor, in practice your editor may also be your previewer. For beginners, the cross-platform TeXWorks editor is a good choice. For more discussion on editors see:
Distributions
A TeX distribution is the whole set of programs and packages that are used to process TeX documents. There are essentially two main distributions: MikTeX (Windows only) and TeX Live (cross platform).
For differences between TeX Live and MikTeX for Windows see:
If you use a Mac, the TeX Live distribution on the Mac is called MacTeX and is essentially a complete TeX Live distribution with some extras for use with the Mac. There is also a smaller version called BasicTeX, but for beginners the full installation is to be preferred. For more on this see:
On Linux systems, you can usually install a TeX distribution using your regular package manager, but this is often out of date. Most people here install TeX Live directly and then use its package manager to update packages. For more on this see:
Engines
There are three main engines for TeX (or LaTeX): pdfTeX, XeTeX, and LuaTeX. For most purposes, pdfTeX should be fine unless your work involves non-European scripts, in which case XeTeX is almost a necessity. For more on these differences, see:
Previewers
As mentioned above, many editors contain previewers themselves, but some do not, or are usable with external previewers. For more discussion on this, see:
Bibliographies
The one other important part of using TeX for academic purposes is bibliography management. Here there are two components: some sort of external program for managing a bibliography, and tools that are part of your TeX distribution used to interface with LaTeX packages for bibliographies. In this case the workflow is the following:

Bibliography managers
Bibliographic entries are stored in a .bib
file. This is just a plain text file which can be edited by hand, but most people prefer to use a GUI reference manager. The most popular of these are
- JabRef (cross platform)
- BiBDesk (Mac)
For more discussion of this see:
LaTeX packages for biliographies
There are two main ways to deal with bibliographies in LaTeX: natbib+bibtex
and the newer biblatex+biber
. For extensive discussion see:
Miscellaneous advice
Once you get going on things, you may also want to investigate systems for managing your work and files. The following question might be of help: