Learn English – Can you say “Our results speak for themselves” if you want to make clear that the results are obvious

When someone is trying to explain a concept and use terms that are far too technical for the average person to understand (like your excellent "click the red button" example!) they are often asked to "Speak in layman's terms". They're being asked to stop using technical jargon, and explain the concept in terms most people will understand. This is a very common expression, and I believe the one you are looking for!

There are myriad ways to express a sentiment similar to the one you describe. Here are a few examples:

The above is purely for your information.

This is solely by way of information.

I write this simply to keep you informed of the situation.

. . . keep you apprised . . .

. . . keep you in the loop.

In my experience (mainly in the world of business), including this sort of phrase in a letter serves to clarify that the recipient is not expected to take specific action at this time. If you want a more general phrase to accompany an informative letter, you might also try:

I hope you find this useful.

By way of agreement with commenter jmoreno, I will add that the most similar practice I have observed in AmE (especially in the business world) is to introduce information that is included purely for information's sake. Often this will occur as early as the subject line of an email, which could begin with “FYI:” without appearing too informal.