How to add several authors with different affiliations in beamer?

Yes, something along those lines:

\author[shortname]{author1 \inst{1} \and author2 \inst{2}}
\institute[shortinst]{\inst{1} affiliation for author1 \and %
                      \inst{2} affiliation for author2}

See documentation for Beamer class (page 94, v3.10).

The second solution provides proper use of font for superscripts.

\author[shortname]{First Author \textsuperscript{1} \and Second Author \inst{1, 2} \and Fourth Author \inst{2,3}}
\institute[shortinst]{\textsuperscript{1} ITMO University \and \inst{2} University of Whatever \and \inst{3} Whatever Institute}

Gives the following -- pay attention to the superscripts font. The first one looks correct.

Here's another solution:

\title{\huge xx}
\author{Author1 \textsuperscript{1,2},Author2 \textsuperscript{1,2,3}}
\institute[A]{\textsuperscript{1}Dep of X\\ %
\textsuperscript{2}Division of X \\ %
\textsuperscript{3}College of X
}