When you shart up lyx at the command line prompt, the following splash screen appears:
Now, open up a new session by clicking "New..."
You can select from any of the following Styles (use the pulldown menu below the File/Edit/Insert)
More styles ...
Even more styles ...
To create an inline math equation, select "Insert/Math/Inline Formula"
Make the Maths Panel visible by selecting "Insert/math/Math Panel"
By inserting characters from the panel, and by selecting "Insert/Special Character/Subscript or Superscript" you can build complex equations
You can align the equation by selecting "Layout/Paragraph/"
By selecting "Insert/Math/Display Formula" you get a displayed equation, that is, on its own line
Select "Layout/Preamble" to insert any special commands. For example, I have inserted the command "\usepackage{times}" to request that the times postscript fonts be used in PDF output ...
Once you have crated your TeX document, select "View/PDF (pdflatex)" to bring up the document into Adobe Acrobat.
This is what it looks like in Adobe Acrobat
You can also export it to a LaTeX file by selecting "File/Export/LaTeX". It will save it as a .tex file in your home directory.
Here is what the LaTeX source looks like. Note, all of the TeX commands begin with a backslash...
You can latex the file by typing "latex file" or "latex file.tex" at the prompt.
Alternately, you can type "pdflatex file" at the prompt, and it will generate a .pdf file of the same name. If you move this to your public_html directory, and change its permissions (chmod 644 file.pdf) you can view it in your browser!
There is one more option, "latex2html file". This will crate an html file in a directory of the same name as your input file.
If you cd to this directory, and look at the file index.html, you will see a (crude) approximation of the document, where all the equations have been replaced by gifs (or png files, in this case)