In general it is better to use either `` and '' to start and end quoting or packages like csquotes and babel. The latter gives you a great support for many languages and their quotes.
However, if you, and the packages you use, don't use the " mark for anything else, you could just define it to automatically insert the above start and end quote marks:
\documentclass{article}
\newif\ifquoteopen
\catcode`\"=\active % lets you define `"` as a macro
\DeclareRobustCommand*{"}{%
\ifquoteopen
\quoteopenfalse ''%
\else
\quoteopentrue ``%
\fi
}
% Deactive with: \catcode`\"=12\relax % changes `"` back to normal
\begin{document}
\section{About "quotes"}
A "quote" is a "quote" is a "quote".
\end{document}

The quotes will automatically open and close.
The quote status can be manually set using \quoteopenfalse and \quoteopentrue.
This behavior is local to the TeX group, e.g. local to an environment.
If this is not wanted a \global can be added before this macros.
This seems to work fine in section titles and also works with babel. However babel sets the language at \begin{document} which might overwrite " again. In this case the macro should be (re-)declared afterwards.
It shall be noted that this might break code which writes the " in an non-text context to the .aux or other auxiliary file.