Server settings. Notice the port is 993, the username is "email@example.com", SSL is selected, and "Use secure authentication" is not:
Here's the login box (notice the weird login account "firstname.lastname@example.org@imap.gmail.com"). Also, this doesn't use your Case credentials through login.case.edu; it uses the GoogleApps Fat Client Password (so don't use your Case credentials):
That covers the basic setup. I would recommend following these tweaks from lifehacker.
Set your "Sent Mail" and "Drafts" to Gmail-default instead of Thunderbird default:
Use Gmail's "Spam" folder instead of Thunderbird's "JunkMail":
And this last one is a little bit trickier to do, but it is covered in lifehacker's post – use Gmail's Trash folder instead of Thunderbird's:
After you do all that, you can delete (from GMail's webmail) the labels "[Imap]/Trash", "[Imap]/Sent", and "[Imap]/Drafts".
All in all, it works fairly well. I expected it to be slow, but it really hasn't been. I had always thought of IMAP as an intranet protocol not suitable for the internet. Yahoo! tried once but had to shut it down. I guess if anybody can do it, it's Google.