Symbols instead of numbers as footnote markers

This can be done by redefining the output of the footnote counter:

\renewcommand*{\thefootnote}{\fnsymbol{footnote}}

If you would like to switch back to Arabic numbering, you can do it by

\renewcommand*{\thefootnote}{\arabic{footnote}}

especially if limiting by grouping (curly braces) would cover a too wide scope.

It may be desirable to reset the counter after such a change, such as by

\setcounter{footnote}{0}

Use the footmisc package, with option symbol.

here is small example:

\usepackage[symbol]{footmisc}

\renewcommand{\thefootnote}{\fnsymbol{footnote}}
\footnote[num]{text}

instead of num you can put the number of the symbol you like:

1   asterisk        *   2   dagger      †   3   double dagger       ‡
4   section symbol  §   5   paragraph   ¶   6   parallel lines      ‖
7   two asterisks   **  8   two daggers ††  9   two double daggers  ‡‡

You may also want to reset the footnote counter for each page. People are not familiar with the symbols beyond the double dagger, and more than (at most) 16 footnotes in a single chapter will result in an error message. To reset the counter per page, either use the footmisc option perpage or the following code:

\usepackage{perpage}
\MakePerPage{footnote}