In reply to Jon Stewart:
> Climb them.
> You're not going to find any better training for climbing overhanging routes than climbing overhanging routes. If you do enough, you'll naturally pick up the body positions to make it efficient, but to speed this up a bit you can think about climbing-on-opposites and using egyptians as much as possible
what Jon says, especially for efficiency, climbing quickly, and clipping 'on the move'. Beyond this, a core workout on rings or TRX and regular sessions on a fingerboard is worthwhile, especially getting your muscles into the 'habit' of taking your body weight on small edges. Footwork is just as important here, esp. Toe and heel hooks in body tension. Worth doing some specific training nights at a bouldering centre.
Maybe a bit obvious, and we don't put it in our profiles, but I found shedding some pounds also yields dividends ;-(