Great idea. You don't say where you are from, so it's hard to know what you do/don't know already.
I went in late Feb to early Apr of 2004, and had mostly nice weather. By the end it was getting a little on the cold side in the mountains, so try to get the big passes done before it starts snowing.
Pedaler's Paradise is a great map book w/info about roads, distances, topography and services. I also had the Lonely Planet guide, and found the general information useful but the specific ride recommendations were too limited - you can pretty much just go anywhere on the south island and be happy cyclists, so don't worry too much about planning.
One month is barely enough. Be prepared for wind, rain, sun, snow, beaches, all in the same day. And ice cream. It's hilly, the towns are close together and often have some kind of indoor accommodation - room above the pub, backpackers, and there are lots of nice clean holiday parks, which usually have a kitchen. Roads are nice, traffic is friendly and sparse except around the bigger cities (Chch).
Very low gearing is helpful, it's not uncommon to encounter 15-20% grades. DOn't worry about training, you'll be fine, you can always do short days when you are tired, and there is plenty to do on a day off.
Oh and the people really are as friendly as you have heard.
Have a great tour!