I use Fraps for recording directly from the game, and Adobe Premiere Pro 2.0 to edit the video, add text lines, add music etc. Other video editing tools will just as well do fine. Whatever you are used to. Premiere is a bit expensive for the hobby user, but Microsoft Movie Maker, provided with Windows XP and Vista, are also usable.
Then I use Windows Media Encoder 9 (free tool) to turn the resulting video into a smaller version, usable for streaming from a Website. The encoder is built into some video editing tools like Movie Maker. The original resolution of 1024x768 at which the video was captured by Fraps is brought back to 800x600, and I use 2 Mbps video bandwith and 64 kbps audio. You can even try 1.5Mbps for the video.
This video can then be uploaded to YouTube.
The most recent one I made is the tutorial of mission 3, which can be found here:
http://www.vstepvideos.com/ShipSim2008/video/
It's a lot of fun once you get the hang of it!
I encourage pro's and amateurs alike to try it out. The most creative part is where you capture your scene in the game, using a mission or free-roam with certain weather settings. Once we release the Editor, on which we are still working, you will have even more Director's options to create your own storyline.