First open Notepad and create your desired signature.

Save this text file in a familiar location on the hard drive.  I put mine in Documents.  Next open Thunderbird and click on Tools Account Settings.

Keeping the default dialog box open, in Default Identity check Attach this signature:  Then browse to the location where you kept the signature text file and click OK.

Now the signature will show up any time you create a new email message.

There are also several cool Add-ons for Thunderbird for further manipulating your email signature.