Semi-Short answer:
- What you need to know as a beginer:
LaTeX is a typesetting system that can be considered a "programming language for pdf (and not only) production". You can use many variations of this language like pdflatex, XeLaTeX, lualatex etc. In your case the file "monthly-template-1.tex" of the first link is a file that can be compiled with pdflatex and so you dont really care at this moment on XeLaTeX or other variations.
- What files you need for your project.
The most of the files that you will use in your project are already installed on your PC during your MikTeX instalation. You don't have to worry of where they are stored or of their content. MikTeX will find them and use them as needed.
There are some additional files that used often. These have the extension
a. "cls" and are used in documentclass command [The first command of a latex document that determines the basic structure of the document (like book, or article or whatever... but in many cases an article or a book is already defined by TeX core and you don't need such a file)]. This file (if you don't use a standard document class) have to be stored in your project's folder (the folder that contains your main file).
b. "sty" and are often called packages that been included in your code via the command \usepackage{example} (This will require an "example.sty" file in your project folder). The "maa-monthly.sty" file that contained in your second link is such a file and called by your main document file (monthly-template-1.tex) in its second row. These files has to be included where our installation takes care to store them (if they are standard packages that comes with our installation) or we have to save them in the folder of our project. (Our project will generate many files during compilation [even if we start with just one "main" file ] and it is better to enclose it in a folder).
(In case you want to use again and again a sty file in several projects, you could save it inside your texmf folred -See @AlanMunn comment below- [But if you want later to sent the project to a friend don't forget to include this sty file too])
- Compiling your project.
This is a procedure that is depended on your editor (if you use a GUI editor interface for your compilation and your editing). For miktex I don't know to tell you, but I suppose there is a button that you press to compile your code using pdflatex or other miktex specific command. The thing you have to know is that independed of your editor, if you run from a command line
pdflatex main.tex
where "main.tex" is your main project file (the one that contains \documentclass command) the compilation will start, and if no errors or conflicts are in the files used, a file named "main.pdf" will be produced independed of the editor you used.
Hope that helped.
pdflatexon the first file (from inside the TeXmaker or the TeXworks or from a command line like "pdflatex monthly-template.tex") a pdf file with the name "monthly-template.pdf" will be created as an example of the template. You can use it as a base of your work and change its contents on your needs – koleygr Oct 16 '17 at 17:49.sty(that is available online) in order to compile a document, which has the same suggested solutions as in the linked duplicate. Your point (2) even references this. Of course, I'm ignoring here the "How to download?" question, as this should be straight-forward for anyone using the Internet. – Werner Oct 16 '17 at 19:20