There are several ways you can go about it. If you want your tutorial to be a view of the computer screen, there are screen capture programs out there that will record what you do onscreen. The one that immediately comes to mind is Camtasia, though I am sure there are others (possibly some of which are open source). If you look back through the posts here you'll find a thread that talks about Camtasia and gives a link to a free version of it, I believe.
You could also use a video camera to capture stuff outside the screen, or point it at the monitor instead of using a screen capture app.
Once you have your footage, you can record a voiceover (if you didn't record the audio while filming). Then, you can use a program like Windows Movie Maker (or Sony Vegas/Adobe Premiere) to edit your video and put in text subtitles or overlays. Finally, upload it to Youtube or a similar site for the world to see!
Definitely try the free version of Camtasia, Yudit. I used it a number of times to post scrolling scores along with music in The Listening Room. Very easy to use. Select the area of the screen you want to capture, and away you go.
Music tutorials might be a tad bit trickier if you want to record what's coming right out of your soundcard and the microphone at the same time... at least I couldn't figure out how to do it... (gotta be a way somehow though...)
Maybe Camtasia has changed things, but the free version I downloaded a couple of years ago is still working and doing everything I need. Here's their site - you could look around if there's still a free trial which doesn't expire:
I used video editing software (there's always a free app with Windows) so that the music would be of high quality for the posts I was talking about. If I'd wanted to add a voice track, I would have used Sonar.
A bit of poking around with CamStudio and Camtasia - you'll figure out what you need, Yudit.
Be sure to check out the free programs folks listed here - Seems that Camtasia doesn't have the free version any more, just a free trial. I'm Very fortunate that the V.3 program I got in 2007 was free and remains completely functioning. But I'm sure these freebies will get you what you need - a simple way to make video files from whatever part of the screen you want.