That's the way to do it using traditional system calls. You can make your life a lot easier using IO::Socket. For instance, here's the preamble in your program:

use IO::Socket::INET;

my $socket = new IO::Socket::INET (
                LocalPort => 8069,
                Proto     => 'tcp',
                Listen    => SO_MAXCONN);

while ($client_socket = $socket->accept())
{
        print "Connection received from ",$client_socket->peerhost(),"
+\n";

        # Do stuff with the $client_socket...
}
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You've assigned $SIG{CHLD}, which implies that you're doing some kind of fork(), but this is not done. Maybe this was stripped from the example. If you're not forking, you won't need it.

As for a "tail -f" equivalent in Perl, try this:

$good = 1;

while ($good)
{
        while (<$LOGFILE>)
        {
                 $client_socket->print($_) || $good = 0;
        }
        seek ($LOGFILE, 0, 1);
        sleep 1;
}
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There is a lot of other things you will want to handle if you are using more than one connection, but this is the basics.