I've had to point a couple of beginners in the right direction through the years and most of them are presumed dead now, so here's my advice:
I'm with Snort, depends on what you want to do.
Trad: Learn to like whiskey and suffering and then proceed with Snort's advice.
Sport: If you're starting out, forget all the hardcore training for now. After you've learnt how to use the basic gear, just climb as much as you can (indoors and outdoors both good, whatever gets you psyched) and learn how to MOVE when you climb first. If you climb a good variety of stuff and keep a close eye on the other climbers also, your weaknesses will become clear quickly, i.e. your finger strength obviously sucks or you flop your feet around too much and Voila! you have an obvious thing to train which will result in improvement.
Bouldering: If you can boulder lots in the gym and outside and restrain yourself from doing crazy moves outside your abilities and getting horribly injured you will get very strong and learn to move very well - probably the best physical climbing training you can do, especially when starting out. Except the whiskey drinking (See: "Trad" above) , that you have to train very specifically and hone your skills over a long period of time - think Mr Miagi / Daniel Son. And just remember no one ever aspires to be a boulderer.
Only joking about the ppl dying, this is just what I start assuming when I don't hear from people in a while. You guys know who you are
