The short answer is that there is no easy conversion for a completely general case. LaTeX2.09 style files are very much a mix of formatting and 'additional' code, even more than is the case with LaTeX2e.
More specifically, the LaTeX2.09 style in question has never been converted into a LaTeX2e class. That means that there the change
\documentstyle{res_yy}
to
\documentclass{res_yy}
is not possible: the later does not exist. That leaves you needing to recreate the layout and macros provided by res_yy in LaTeX2e. This is certainly possible, but I suspect that the effort is not really balanced off by the outcome. The amount of work needed to do the conversion seems at least equal to starting either from article or a specialist CV class.
res_yyclass for LaTeX2e. – Joseph Wright♦ Oct 1 '11 at 7:25\input article.styin a (renamed) copy of res_yy.sty and then load it with\usepackageand look what happens. If you want to use hyperref you should also remove the\nofilescommand. – Ulrike Fischer Oct 1 '11 at 10:37