I have introduced LaTeX into our organization and quite a number of other people at a personal level over the years. In academia it is almost tradition that LaTeX is introduced via word of mouth and that the person that made the introduction helps with the first steps.
Most "non-technical" people use Windows or maybe Macs and probably are not old enough to remember operating a computer via a command prompt. You can assist your friend tremendously by helping to install a full MikTeX installation. If you noticed I mentioned full, as the biggest frustration of new users is setting up everything and is best to avoid errors due to missing packages at the beginning. MikTeX can update on the fly, but on a slow internet connection, it often fails. Use the default Texworks editor, as spell-checking and highlighting are good.
Provide an empty template, with maximum one or two packages. Provide also a reasonably sized document that works (must have an index and contents) and relates to their work.
Give them a bit of a coaching how everything works and help them put their first document together. Newcomers get very excited when they see the first document with contents, index and footnotes. Most non-technical people find it almost impossible to do this with Word or Libre Office.
Introduce images early and the idea of floats. Leave tables as the last item under discussion and well after the newcomer has done a bit of LaTeX work.
I think we are the only Construction Company that uses LaTeX for our reports. Most users have an Engineering background and some of them have good computer skills. As they are a mix of 32 nationalities skills vary tremendously. Strangely enough one of our secretaries took to it very easily but not our IT guy.
As to your question about introductory material, the best is a good book (after you have whetted their appetite a bit to want to use LaTeX to its full capacity).
You asked for the packages... Well the link you provided is prepared using the exerquiz
package from The AcroTEX eDucation Bundle (AeB)
. Following is a screen shot from the aeb
manual.

For more details do a texdoc acrotex
from the command line.
EDIT: The links for sample files as given by the aeb
manual are:
http://www.math.uakron.edu/~dpstory/webeq_ex.html
Example Files for AeB
This is a screen shot from manual again showing the links:

Best Answer
As a Mathematics/Engineering student approaching the end of my undergraduate career, I can say that typesetting my Homework was a pain until I had a nice refined template to use. Based on my experiences, I would suggest the following:
Provide your students with a LaTeX template that they can use as a starting point for their homework. Something that has nice features like a "Problem" environment that auto-increments question numbers and has support for sub-problems (parts, a, b, c, etc). Bonus points for nice headers/footers that show the student's name, current problem and "Continued on next page" if the answer is long. Providing a nice template eases the learning curve and can really sell some people on the elegance of TeX.
Absolutely, positively, provide the TeX sources to any assignment or notes page you hand out. One of the most pointless, time-consuming activities I have been forced to undertake is copying problem statements out of a PDF, pasting them into my homework document, and then regenerating all the mathematical typesetting and enumeration markup that did not copy cleanly or at all. Bonus points for using the homework template you developed to provide questions- then there is no copying and pasting, students just have to fill in the answer.