use IO::Socket qw( );

my $sel = new IO::Select( $sock1, $sock2 );

while ( my @ready = $sel->can_read() ) {
   foreach my $sock (@ready) {
      if ($sock == $sock1) {
         ...do someththing...

         if (...done...) {
            $sel->remove( $sock1 );
         }
      }

      elsif ($sock == $sock2) {
         ...do someththing...

         if (...done...) {
            $sel->remove( $sock2 );
         }
      }
   }
}
[download]

Don't use read or <$sock> in combination with select. Their buffering nature will interfere.

You might want to read into a buffer, because you're not guaranteed to get an entire message or no more than a message in each sysread.

sysread( $sock, $buf, 32*1024, length($buf) )
   or do { $sel->remove( $sock ); next; };

while ( my ($msg) = $buf =~ s/^(...)// ) {
   process($msg);
}
[download]

All together:

use IO::Socket qw( );

my $sel = new IO::Select();

my %clients;
for my $sock ($sock1, $sock2) {
   $clients{$sock} = {
      buf => '',
      # ...
   };

   $sel->add( $sock );
}

while ( my @ready = $sel->can_read() ) {
   foreach my $sock (@ready) {
      my $client = $clients{$sock};

      our $buf; local *buf = \( $client->{buf} );

      sysread( $sock, $buf, 32*1024, length($buf) )
         or do { $sel->remove( $sock );
                 delete $clients{$sock};
                 next;
               };

      while ( my ($msg) = $buf =~ s/^(...)// ) {
         process($msg);
      }
   }
}
[download]

Updade: Added tip on how to read socket.