LaTeX is a document markup language and a word processor that's used for the communication and publication of scientific documents in many fields, including mathematics, physics, computer science, statistics, etc. It provides superior document formatting and handling of mathematical notions, thus is THE document preparation system for technical communications.
BibTeX is the reference management software/format that is used together with the LaTeX. BibTeX makes it easy to cite sources in a consistent manner, by separating bibliographic information from the presentation of this information, similarly to the separation of content and presentation/style supported by LaTeX itself.
There are tremendous amount of information available online for learning LaTeX. Here’s a list of good self-learning materials from various sources.
The Not So Short Introduction to LaTeX
LaTeX for Complete Novices
The LaTeX wiki book
The Art of Problem Solving's LaTeX Wiki
Getting Started with LaTeX
Comprehensive LaTeX Symbol List
LaTeX Bibliography Management
Tame the BeaST: The B to X of BibTeX
LaTeX packages and editors are required in order for proper LaTeX typesetting, most of which are freely available online. Here are some commonly used LaTeX systems at the moment.
Comparison of TeX editors from Wikipedia
Although BibTeX is able to manage the references in plain text form (.bib format), it is always a good idea to have some tools with GUI frontend for better visualization and easy integration with LaTeX editors.
OS-independent Java GUI frontend for managing BibTeX and other bibliographies.
BibTeX editor and reference manager for MacOS.
Intended for experience Linux users, BibTool provides features similarly to JabRef, and more functions as a tool for manipulating BibTEX files.
Another free and open-source reference management software.
Cloud-based reference management software from Elsevier.
Similar to a Linux system, LaTeX uses packages to manage/extend the functions and features available to users. Though a base LaTeX install will get most commonly used packages covered, users may still be required to install certain packages when needed. (Fortunately, the widely used LaTeX systems such as MiKTeX handle such package installations automatically with minimum interference required from the users.)
AMS-LaTeX & AMS-TeX
A list of packages consisting file styles, fonts, author packages developed by American Mathematical Society, for the convenience of authors.