How to write a footnote attached to the author in a LaTeX paper?

I think the command you're looking for is \thanks

\documentclass{article}

\title{My great paper}
\author{One author\thanks{some info} \and Another author\thanks{more info}}

\begin{document}
\maketitle

\end{document}

If your document class is amsart then the syntax is a bit different

\documentclass{amsart}

\title{My great paper}

\author{Fist author}
\thanks{The first author wants to thank someone.}

\author{Second author}
\thanks{The second author wants to thank someone else.}

\begin{document}
\maketitle

\end{document}

Note that in the \thanks command you have to explicitly mention which information corresponds to which author, since no footnote “marks” will be printed with the acknowledgements. This is apparently the preferred style for AMS as discussed for example at the The AMS article document class.

I've been doing something similar to have different authors with the same affiliation and have adapted an example from Anthony Liekens.

\documentclass{article}
\usepackage{hyperref}
\newcommand{\footremember}[2]{%
   \footnote{#2}
    \newcounter{#1}
    \setcounter{#1}{\value{footnote}}%
}
\newcommand{\footrecall}[1]{%
    \footnotemark[\value{#1}]%
} 
\title{How to bowl properly}
\author{%
    The Dude\footremember{alley}{Holly Star Lanes Bowling Alley}%
    \and Walter Sobchak\footremember{trailer}{probably in a trailer park}%
    \and Jesus Quintana\footrecall{alley} \footnote{Mexico?}%
    \and Uli Kunkel\footrecall{trailer} \footnote{Germany?}%
}
\begin{document}
\maketitle
The whole example is taken from \href{http://anthony.liekens.net/index.php/LaTeX/MultipleFootnoteReferences}{anthony liekens}\ldots
\end{document}