If I wanted to take a Greek train from say Thessaloniki to Sparti or Tripolis in the Peloponnesus how would I go about it? Would I need to de-train at Corinth or does the train go across the canal? How long a trip would it be? How are Greek passenger trains?

No trains go to Sparti. I believe Kalamata station and line is under repair. You might be able to head to Patra, Olympia, Tripoli or Argos by train. If you never taken a train in the Peloponnese, be prepared for an adventure (not the good kind) I would suggest an air conditioned bus. A bus ride from Athens to Sparti takes about 2.5 hours and stops at Corinth Canal for passangers to take photos!