$string !~ m{^/[*/]}; # ^-beginning of the line, /- a slash [*/]-character class containing * and /

See   perldoc perlre.

Update:   !~   negates the match.

Update2: Thanks to Corion who pointed out that my approach didn't catch multiple line comments.

# a loop could do it like this:

$block_comment = 0;
while ( <INPUT> ) {
    if    ( m{^//}  ) { next; }
    elsif ( m{^/\*} ) { $block_comment = 1; next; } # start block
    elsif ( m{^\*/} ) { $block_comment = 0; next; } # end block
    elsif ( $block_comment) { next; } # inside block
    else { ... do something with the line, that is no comment ... }
}
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Cheers, Sören