Look here: Twisted Web in 60 seconds. That's a group of blog posts describing step by step how to do lots of common stuff with Twisted, all written by Jean-Paul Calderone, the biggest contributor of Twisted. It's really where you should start.
Its worth remembering that Twisted programming is more of a thinking paradigm than a programming one. Also, it's worth doing away with the client server model too - in Twisted there's just one broker talking in either direction to another.