How can I place a one-column-abstract in a two-column document?

This should make the trick. Important Note: This is a copy-paste from: I've just tested it

\documentclass[twocolumn]{article}
...
\begin{document}
... % \author, etc
\twocolumn[
  \begin{@twocolumnfalse}
    \maketitle
    \begin{abstract}
      ...
    \end{abstract}
  \end{@twocolumnfalse}
]

If you use the multicol package then you can easily mix different column format

\documentclass{article}
\usepackage{multicol}
\usepackage{lipsum}% for dummy text

\begin{document}
\begin{abstract}
\lipsum[1]
\end{abstract}
\begin{multicols}{2}
\lipsum[2]
\end{multicols}
\end{document}

The \twocolumn-command takes an optional argument, which will be printed in one-column-mode.