How can I use gpg to both encrypt my email and prove my identity?

What is GPG?

How do I use it with Windows and Thunderbird?

assuming you have Thunderbird installed already.

go to ​http://enigmail.mozdev.org/
click on "download"
pick the appropriate operating system and email client from the scroll down

you can see what version of Thunderbird you have by:

-go to Thunderbird
-click on "Help" (File menus at the top)
-"About Mozilla Thunderbird"