What really helped me improve my typing speed is...
gaming. I learned to type by using the keyboard for games like starcraft 2, chatting in skype, and leaving comments on forums. Practice, in whatever form, is the best way to improve typing speed.

When my fingers hurt after too much time on the keyboard, I...
stretch them out! If you leave your hands sitting at the keyboard and typing without going through different ranges of motion, they will get tense and start to hurt.