Creating customized footnotes

This can work only if you use a “per page” numbering of footnotes. Next, the typesetting of the marker must be modified.

\documentclass{article}
\usepackage[perpage]{footmisc}
\usepackage{etoolbox}

% three should be sufficient
\DefineFNsymbols*{asterisks}{*{**}{***}}
\setfnsymbol{asterisks}
\renewcommand{\thefootnote}{\fnsymbol{footnote}}
% we want a nonbreaking space before the marker in text
\preto\footnote{\unskip~}
% we want the marker normal size and not superscripted, with )
\makeatletter
\renewcommand{\@makefnmark}{\mbox{\normalfont\@thefnmark})}
\settowidth{\footnotemargin}{***) }
\patchcmd{\@makefntext}{\hss\@makefnmark}{\hss \@makefnmark\ }{}{}
\makeatother

\textheight=2cm % just for the example

\begin{document}

First footnote\footnote{Some long text that should wrap
across at least two lines; just add text just add text
just add text just add text just add text.}.
Now another footnote just to see what happens\footnote{Try this.}.

\end{document}

Here's a setup with \textasteriskcentered (providing for *,**,*** at the moment only) and using footmisc.

There's a wiley set of footmisc, which has *, ** already, but not ***, if this should be needed at all.

\documentclass{article}


\usepackage[symbol]{footmisc}


\DefineFNsymbols*{asterisks}{\textasteriskcentered{\textasteriskcentered\textasteriskcentered}{\textasteriskcentered\textasteriskcentered\textasteriskcentered}}
\let\origthefootnote\thefootnote
\renewcommand{\thefootnote}{\origthefootnote)}

\begin{document}
\setfnsymbol{asterisks}
A footnote on foo\footnote{foo} and another footnote on foobar\footnote{foobar} and yet another one\footnote{foobar foo}
\end{document}