Mozbackup is a very simple freeware app to backup up your Firefox and Thunderbird profiles, and restoring them or exporting them to another computer.
To use, install Mozbackup and run. It will take you step by step towards backup up the profiles you want. Make sure that both Firefox and Thunderbird are closed when you do this, by the way (it'll warn you if it's open). In the end, it saves a .pcv file, which is really just a zip file with a different extension.
To restore a backup, just run Mozbackup again and select Restore a profile instead of Backup a profile. Again, step by step. To import a backup into another PC, install MozBackup into that computer and restore.
My only gripes about MozBackup are that it only works for PC; no linux or OSX support, which is one of the reasons Mozilla's apps are so useful and recently ubiquitous. Likewise, I'm not fond of the fact that MozBackup requires its own program to be installed. I guess it's too reflexive to have it create a backup of the very profile in which it's located, but if it were an extension for Firefox and Thunderbird it would be so much simpler to use. I'm not crazy about installing programs that I use less than once every few weeks.
Overall, though, there is no simpler way of moving and backup up profiles from one PC to another than MozBackup.