Entering compatibility mode

You run your LaTeX job, and it starts by saying

Entering LaTeX 2.09 COMPATIBILITY MODE
followed by lines of asterisks and !!WARNING!!.

This means that the document is not written in “current” LaTeX syntax, and that there is no guarantee that all parts of the document will be formatted correctly.

If the document is someone else’s, and you want no more than a copy to read, ignore the error. The document may fail elsewhere, but as often as not it will provide a dvi or pdf that’s adequate for most purposes.

If it’s a new document you have just started working on, you have been misled by someone. You have written something like:

\documentstyle{article}
or, more generally:
\documentstyle[options]{class}
These forms are (as the warning says) LaTeX 2.09 syntax, and to get rid of the warning, you must change the command.

The simple form is easy to deal with:

\documentstyle{article}
should become:
\documentclass{article}
The complex form is more difficult, since LaTeX 2.09 “options” conflate two sorts of things — options for the class (such as 11pt, fleqn), and packages to be loaded. So:
\documentstyle[11pt,verbatim]{article}
should become:
\documentclass[11pt]{article}
\usepackage{verbatim}
because 11pt happens to be a class option, while verbatim is a package.

There’s no simple way to work out what are class options under LaTeX 2.09; for article, the list includes 10pt, 11pt, 12pt, draft, fleqn, leqno, twocolumn and twoside — anything else must be a package.

Your document may well “just work” after changes like those above; if not, you should think through what you’re trying to do, and consult documentation on how to do it — there are lots of free tutorials to help you on your way, if you don’t have access to a LaTeX manual of any sort.