Now there is one tricky on the weird, and that is if you have opted for Google's 2 step verification. If you have, it means your password will not work in Thunderbird...but all is not lost. From some poking around in my Gmail settings (you will need to log into Gmail in a browser to find them), I found the workaround - Google will give you a super special password for apps like Thunderbird which don't play with all that 2 step shuffle stuff.
To obtain the magical key, you first must log into Gmail and click your email address in the top right corner, then "Account", that will open a new window/tab. Now go to the "Security" item in the left side, and that will open those options. At the bottom of the Security settings page look for "Connected applications and sites" with a "Manage Access" button - did you find it? Cool now do what comes naturally and click it - and then log in again because Google says so! Here is where you can find the key to make Thunderbird work with Gmail. You will see a item called "Application-specific passwords" where you can generate a special password that Thunderbird can use. Just put a name in the box (may I suggest "ThunderChicken") and then click "Generate Password". Now it will spit out the magic password which you can go back and put in as your Gmail password in Thunderbird.