If you account was truly hacked, you probably can't even get into it because someone changed the password and the email associated with it. But if your Twitter name is suddenly tweeting spam or sending DM messages to people you follow with links and messages like "Someone is talking smack about you.. [link]," then your account has been compromised by some rogue Twitter application that was activated while you were surfing the web somewhere. The app is allowed to connect to your account via Twitter's authorization system and we have to fix it. Fast.
Here's the fix
Go to Twitter.com > Settings > Applications
If you recognize something you've authorized only recently, and it's some minor app, this is probably your culprit. Just click "Revoke Access" next to it. But if you have any doubts, revoke access to everything and anything you don't recognize or absolutely need. It's easy enough to reauthorize each app as you need them. Popular applications like Tweetdeck will be safe so you can skip those.
Change your password immediately
In theory, Apps don't use your password, but since a rogue App is dishonest anyway, you have to assume it could have gotten your password somehow.
Remember, good strong passwords are at least 8 characters with a mixture of characters, capitalization, numbers, and/or some symbols. Don't use real, properly spelled words if you can help it. Example: HOrz-8a8-Fthrz. Using a product like LastPass can keep your passwords for you in a safe manner. Google it.
Don't be too quick to authorize an App. Ask yourself, "is this thingie-doodle really worthwhile, or just some stupid game or gimmick that really isn't worth the hassle if it's actually malware?"
But don't be too paranoid, either. Many Apps are fun and useful, and most of the time the compromising is just a mild annoyance, but not harmful enough to really worry about. Having someone receive DM spam is not like someone hacking your bank account.Tweet