I get asked this enough that I guess I should put it in my blog, even though a google search will show you how pretty quickly anyway...
The process is pretty simple. Once you have firefox installed on the new machine, you need to locate your original Firefox profile, then copy it to your new computer, delete your NEW computer's profile, then rename your copied original profile to the new machine's profile name.
So let's clarify those steps:
1: Locate your original profile. It will be in your application data folder for your username. To get there, go to the start menu, run (or on vista, search) enter: %APPDATA% then enter.
then go into the mozilla\firefox\profiles folder
find the folder that ends in .default. If you are NOT using profiles in Firefox, this is what you need. IF you are using profiles, you probably have no need to read this.
2: Copy the folder you just found to your NEW computer's appdata\mozilla\firefox\profiles folder. (at this point you will NOT be doing any more work on the OLD computer)
3: Copy the name of the NEW computer's pre-existing .default folder.
4: Rename that NEW computer's pre-existing .default folder (putting a .OLD on the end of the name works well)
5: Rename the folder you just copied from the OLD computer to the name of the NEW default folder.
6: Start Firefox, and you should be good to go. You can now delete the default.OLD folder if you want, or leave it. Whatever.