MiKTeX is an "all in one" option for getting you up and running with LaTeX. It is easy to install, and comes with all you need to get started.
Download the installer here. After MiKTeX installs, locate the executable file for TeXworks, which is your interface with LaTeX. It should be in the folder "Program Files\MiKTex2.9\miktex\bin\x64" or something similar depending on which version they are up to. You might want to make a shortcut for it.
If you have a Chromebook or something similar, you can try LaTeX Editor.
The first thing to do is to show the line numbers by selecting Format, then Line Numbers from the top menu. This will help you with troubleshooting. While we are at it, let's make having line numbers the default. At the top of the TeXworks window, select Edit, then Preferences. Select the "Editor" tab and check the "Line numbers" box. Click OK.
\documentclass[12pt]{article}
\begin{document}
Hello world!\\
$ax^{2}+bx+c=0$
\end{document}
Now at the top of TeXworks you will see a green button. This is the "Compile" button. Next to that you will see something like "pdfLaTeX+MakeIndex+BibTeX." Click on the downward triangle next to that and choose "pdfLaTeX." Then click on the green "Compile" button. You will be asked to save the file and give it a name. Name it test.tex in whatever folder you want to keep your LaTeX files in. After you save a file a new window should open up with a PDF file containing your document. If the document looks OK, MiKTeX is working!
Warning: Every time you click the green compile button, TeXworks will save the file with the last name it was given. This can be troublesome when you use a template *.tex file your instructor gives you. Before you click the green compile button after opening a new file, click File and Save As from the top TeXworks menu to give the file your own name.
In TeXWorks, remove the "$" after the 0 in the quadratic equation and press the green compile button again.
You will see error messages in the Console output screen below your document. Some times they will help you figure out what is wrong, sometimes they won't. When you have an error, you will see a "?" in the Console output. Press ENTER and it will move along, perhaps to another error (press ENTER again), perhaps to the end of the document. The compiler will attempt to fix your error and give you finished output. Often you can tell what your error is by looking at the finished output. Do not be discouraged. Often one small mistake can generate many error messages.