How do I telnet into a machine and then to a third one?

smoss has asked for the wisdom of the Perl Monks concerning the following question:

I need to run a script using Net::Telnet which logs into one machine and then into a third machine (because of a firewall) and pull info of the third server. My script always fails after the login to the second machine.

How should I initiate the telnet session on the second machine correctly?

Originally posted as a Categorized Question.

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