When I use an app such as Safari, I can choose to "Tweet" a page and it uses my Twitter account. How do I sign out of that Twitter account so that if I give my device to someone else, they can no longer tweet things on my behalf?
The only way to sign out of an account is to actually delete it, according to the UI. This is tied into the Twitter integration that was part of iOS 5.
To sign out of the account, you need to:
This does not delete your actual Twitter account, it just logs you out and removes that accounts credentials from your device.