What do you use to write letters?
Off the shelf word processors. For example MS Word, or Google Docs. Google Docs has the advantage that it doesn't require any software to be installed, since it runs completely in the browser. It also happens to be free and requires no license. I think MS Word today has a mode where you can do all the editing in a browser too (it may be the "Word 365" version), but I'm not perfectly sure about that, since I have a licensed version installed on my Mac.
Ah, this is where it gets interesting. Scientific papers (for submission to conferences or journals): Until about 15 years ago, I used LaTeX for that. I have not used plain TeX (instead of LaTeX) since the first drafts of my master's thesis, in 1986; the moment LaTeX became widely supported, plain TeX fell completely by the wayside, not only for me, but also in my scientific community. By the way, my master's thesis in 1986 was the last time I wrote a scientific paper that required cutting and pasting the graphs (diagrams) using scissors and rubber cement; since then, all my documents have been done with the graphs included digitally.
Then an interesting transition happened. I can explain when it happened by a real-world example: In 1995, I was the technical editor of a very large scientific paper, a 500-page document that had over 500 authors (and was published as a technical report, in the style of the physics community). It took me about half a year of my professional life to shepherd it through the production process, from collecting little snippets of text and graphs/diagrams from various authors, to camera-ready copy run from a phototypesetter at a large government printing office. This was all done in LaTeX, because the scientists in the community thought it would be the only tool powerful enough to handle it. Ultimately, LaTeX couldn't do it (on the computers available at the time, which was a high-end multiprocessor IBM RISC server running a Unix variant), and we had to do the final dvips run about 100 pages at a time. One member of our team was a publications professional (a technical editor at our publications department), and she was editing another very large paper at the same time, a document of about 900 pages. She did that one completely in MS Word on a Windows machine. It worked about as well as LaTeX: not perfectly, but well enough.
In the last ~25 years, I have worked in computer science research labs (such as HP and IBM labs). Even in those places where everyone is a Unix bigot, the common tool for writing research papers and journal publications has moved from 100% LaTeX to about 80% Word+Docs, about 20% LaTeX holdouts. And that includes theoretical computer scientists and mathematicians.
So my personal advice would be: Use MS Word or Google Docs. By the way, if you need formulas: Both Word and Docs have a "LaTeX compatibility mode" for math. It works excellently, but their native math typesetting handles most stuff pretty well.
The UNIX program was from the beginning troff. Does someone use it?
About 20 years ago, when I started working at IBM, there were still a handful of people using troff. Those were curmudgeons. And a larger handful of people using IBM's internal tool (which is based on SGML, a predecessor / relative of HTML). And a few using FrameMaker. I have not heard of anyone using *roff for anything other than man pages in a decade or two.
How do you install and update it?
To be honest: In the last 20+ years I have not had to install (La-) TeX myself. I know it is exceedingly difficult. I rely on professional sys admins at work for that, as this is not amateur something for amateur hour.
My advice: go to docs.google.com, and get on with life. Or turn writing documents into a hobby.
