easiest way is to use a backup tool like MozBackup how to at http://kb.mozillazine.org/MozBackup and download at http://sourceforge.net/projects/mozbackup/

sorry I forgot to mention that I run Linux and mozbackup is for windows I think.

Then copy your profile. Read this article found by Googling Thunderbird Backup. https://support.mozilla.org/en-US/kb/profiles-tb

1. Select Help(or AppMenu/Help)/Troubleshooting Information, click Show Folder to open the profile folder (Linux). Don't just copy the profile folder, but the folder that contains the profiles, e.g. in Windows you want to copy the Thunderbird folder (two levels up) that contains the Profiles folder, profiles.ini, registry.dat and the Crash Reports folder. The contents may be slightly different in Linux, but they should at least include profiles.ini and a Profiles folder; the latter usually contains a single folder named e.g. asdfg.default.

2. On the new system, launch TB, but cancel any prompts to set up a new account. Select Help/Troubleshooting Information, click Show Folder to open the profile folder, which contains default data. Exit TB and delete the existing Thunderbird folder, and in its place copy the Thunderbird folder created in step 1. Restart TB and find that it reads all the data from the previous installation.

This method applies, with a few minor additions, to moving TB data from one computer to another, with or without the same operating systems.