Start up Thunderbird on the computer you are using.
Delete all the items from your Trash and Junk folders for each account you have in Thunderbird. This will cut down the size of the files and speed up the transfer.
Find the Default Thunderbird Profiles folder on the "old" computer. On Windows XP/2000 this file is located in your root directory (C drive) under Documents and Settings. Select your Username and go to the "Application Data" directory. The file will be in the "Profiles" folder of the Thunderbird directory in the "Application Data" folder (C:\Documents and Settings\[User Name]\Application Data\Thunderbird\Profiles\). On Vista, the file is located here: C:\users\[User Name]\AppData\Roaming\Thunderbird\Profiles\.
Locate your Default Thunderbird Profile folder named "XXXXXX.default" where the X's are a random mix of numbers and letters.
Copy the files in "XXXXXX.default" directly to the "new" computer over the network, or you can use a removable storage device such as a USB thumb drive or CD-R. Don't copy over the directory named "XXXXXXX.default", but just copy the files in the directory.
Download, install and run Thunderbird on the "new" computer. A new Default Profile is created when you run Thunderbird for the first time.
Shut down Thunderbird.
Move the files you copied from the Default folder of the "old" computer to the Default Thunderbird Profile folder ("XXXXXX.default") on the new computer. Again, you're moving the actual files in the old "XXXXXX.default" folder.
Launch Thunderbird on the "new" computer. Your old settings and emails should be available on this new installation.