Normally, Thunderbird keeps addons up to date automatically. You normally don't need to do anything to keep ExQuilla up to date.
If you come here, then probably because that didn't work, so here's how to do it manually:
1. Go to Thunderbird addons page.
2. Click on "Extensions" on the left. Then, next to "ExQuilla", click on [More].
3. In "Automatic Updates", first select "Off", then click [Check for updates].
4. After click [Check for updates], Thunderbird should update ExQuilla to the latest version.
5. Thunderbird will suggest a restart. Don't do that yet.
6. Enable automatic updates, by selecting "On". (This is important for you to get the latest bug fixes.)
7. Finally, restart Thunderbird
Now, your ExQuilla should be up to date. You can verify that by going to the addons page again, as in step 1 and 2.