Someone pointed out in the Nico intro post that all the registration tutorials out there are out of date, so here's an updated one by yours truly.
Making a Nico Nico Douga account 101First, go to Nicovideo: http://www.nicovideo.jp/
Then follow the bouncing ball:
That's it! You're registered, and you should also be logged in. If you log out, or try to watch a video on a different computer, you'll need to login again. Just follow the ball again: