BDAB, is your notebook a Compaq or HP?
Ubuntu doesn't like many of those computers because of their proprietary video.
It will run from the Live CD because it's using a generic driver, but will crash when you try to install.
They won't even run properly with Windoze until you download their video drivers from their website.
I get to work on everybody's broke computer, and I now refuse to work on Compuke or HPs 'cause they are the computer equivalent of an A4LD. They're OK until they break, then might as well trash 'em.
If your computer isn't one of the evil twins, the current version of Ubuntu comes with a built-in program called Wubi. It will be one of the choices presented at installation. It is a great way to try it. Once again, if your computer is built by the evil twins, it likely won't work. (I know that it can be made to work on them, but usually requires a lot of tweaking that most people don't want to deal with)
HERE is a Wubi How-To.
Basically, it will install a complete copy of Ubuntu into a folder on your HD and give you a dual boot menu. Choose Ubuntu at startup and you're running full Ubuntu. If you find you don't like it, start Windoze and go to Add/Remove programs. It will be listed there. Select it and uninstall. You are back to your original Windoze installation.
Typing this on Ubuntu 8.10 right now. At home, I only surf the web with Linux or my Mac.
Good Luck!