Suppose you have a plain-tex or latex file called myfile.tex . How do you
turn that into something people can actually read, i.e. where the
alphas really look like an alpha instead of "\-a-l-p-h-a" ?

The answer is: it depends.

If you're using a PC and have installed MikTeX on it, this is not too hard.
Arrange your screen view so that you have a MikTeX open, and so that
there is an icon for the .tex document you have prepared. Near the
top of the MikTeX display it probably says something like "LaTeX => DVI"
Use the little menu arrow there to select the combination of input and
output files you need: if your  .tex file is a latex file, great; if it's
a Plain TeX file, you'll have to change this so it says "TeX => DVI" or
something. If you want a DVI file, that's great; otherwise you want to
select "LaTeX=> PDF" or whatever. (You can increase the number of options
at this point by going through the "Build" menu at the top; one of its
menu options is "Define Output Profiles", and you can use this to
change the set of options for input and output filetypes.)

When you have selected the right combination of input and output, click
on "Build", then "Current File", then "Build Output". This should produce
new files with suffixes  .pdf (or whatever you selected), as well as
.log and maybe .aux .

Technical note:=============================================================
|| One of the things LaTeX is good at is crossreferencing: you can say things
|| like "As we see in Equation (2), ..." without having to insert the number
|| "2" into the text -- internally, you can refer to the equation with some
|| other label, and then let LaTeX number the equations in order. That's very
|| useful if you're going to be re-organizing your paper, so that such-and-such
|| an equation changes from being the second to the third --- you don't have
|| to rewrite your text references to the equation.  Frankly I don't expect
|| you to need this feature, but you have to know that it exists: the only
|| way to make it work is to go through the process of building the document
|| from the TeX source TWICE. The first time, it will create an extra file
|| called myfile.aux which contains the cross-referencing information; this
|| file will be read in during the second run.
\\================================================


If you're using a PC but not the TeXNiC Center, try doing this.
(I'm assuming you have installed MikTeX; with any other distribution the
steps will be similar.) As above, you want to arrange your screen so you
see an icon for the document, and you also want to see the executable
you will run. In the case of MikTeX, these are pretty well hidden!
From "My Computer" click through to where you installed MikTek (I had
made a directory  C:\Program Files\MikTeX ; yours may be at  C:\  .)
Then click through to  texmf -> miktex -> bin. There are many binaries
(executables) available; look for  pdftex.exe or pdflatex.exe (or tex.exe
or latex.exe if you want  DVI output).

If you just drag your .tex file's icon over the program's icon, the
program will process your file. Your new files (.pdf, etc.) will probably
be in the same directory as the binaries (sort by date and go to the bottom!)
You should move your files out of there and onto your desktop or some other
directory of yours.

(If you're going to do this a lot, you should take the following steps:
   (a) Make a shortcut for the binary file, e.g. on your Desktop
   (b) Right-click that icon -> Properties -> Shortcuts -> Start In :
       Type in the name of a good directory for the output.)


If you're running any version of unix, it's probably simplest to open
a command-line shell and just type     tex myfile.tex   
(or   pdflatex myfile.tex   or whatever).




If you are feeding a .tex document with correct syntax to your executable
program, you should get an output file of the type you asked for (.pdf, etc.)
But if there are errors which make it impossible for TeX to understand
what you meant, then the program will report an error and you will get
no output. (If you are running your TeX program interactively, it may halt
at the first error and give you an opportunity to give it some new
instructions; just type  X  and it will then halt.)

Either in your program's display, or in the .log file it created, you
will find a description of the error(s) it found. You will need to
go back to your .tex file and fix the errors and start the cycle again.
If you can't figure out how to fix the errors, just comment-out the
offending passage %like this
and try again with the rest of your document -- you can ask for TeX help
later and fix the strange passage with someone's help.




If there have been no fatal errors, your program will now have produced
a file (.pdf, .dvi, etc.) which can be viewed with another program.
On Windows, you can often simply click on the icon of the new program;
Windows will try to guess what you want to do with the file, and it
should guess these correctly. On many operating systems, you can attempt
to open these files with your Web browser, since  PDF and some of
the other formats are common types of files on the web, and your browser
may know what to do. Otherwise, try feeding the .pdf files to Adobe
Acrobat, the .ps files to GhostView (GS View), and the .dvi files to
xdvi or yap.exe (Yet Another Previewer).


One thing you may see is that the output isn't what you might have wanted.
TeX does its best but is not clairvoyant and cannot do the impossible.
For example, if you try to include a very long equation which you ask to
be displayed all on one line, TeX can do nothing but (complain and) print
what it can on the line, spilling into the margin as necessary. In TeX
lingo, this is an "overfull hbox". It's considered Poor Form (tm), and
TeX wants you to fix it somehow (e.g., did you really need to put
in so many equations?) Just so you don't miss the opportunity to improve
your document, TeX will put a big black box at the right edge of the
offending line.

Also, if the document included some internal cross-references, TeX is
stuck because it may not know what number your last equation will be
when you say, at the beginning of your document, "As we will see in
our final equation ..." so it will be unable to insert an equation number
there at the beginning. That problem is easy to fix: just run TeX a
second time, and all will be well.


If you have no more corrections to make to your document, then TeX has
done its work. Use your document viewer (e.g. Acrobat) or some other
means to print the document so you can turn it in. Print off another
copy for your mother's refrigerator; she will be so proud of you!

Don't forget to save the .tex file. It will take very little space, and
you can easily re-generate the .pdf and other files from it. You will
wonder, a few years from now, how it was that you successfully got
a subscripted superscript in that one equation in your Math 360 paper,
and so you'll be glad to be able to pull out the old .tex file to see
how it's done.

(PS -- it's like this: $a^{b_c}$. Or check this out: $a^{a^{a^{.^{.^.}}}}$ !)