Dear Spartacus,I now play a 17 fret Lyon and Healy 1925 vintage tenor and used to play a Vega N-style. The tutors John referred to are reasonably good but the best way is to try and find a session with a friendly tenor player (we are a friendly bunch!).
My resonator is more or less permanently "fixed" (it is a "plate" type with five screws securing it) so I can't dampen like Jon. For damping (I never actually bother really!) I therefore use a quickfix metal "damper" that is secured just behind the bridge with a thumbscrew. You can get one of these from any decent supplier like Sully or Andy Perkins (in the UK) or Mandolin Bothers or Elderly in the US.
To get a decent tune won't take too much sweat, just "go for it" (not too fast at first or, indeed in my view, at any time! ...I've seen a few "speed freaks" lose too much subtlety and "feel" at supersonic levels!), the tricky things on tenor banjo are good fast triplets and "cranning" but these will come also with practice.
Good luck with your playing... I play guitar, mandolin, octave mandolin, bouzouki and a couple of other instruments as well but still find the tenor the most "fun" instrument!
Best regards,
mooman