All you have to do is stay very quiet and don't make a move. On the other hand, if you have stuff to say, but don't want anybody to hear you, don't say anything funny, topical, or - and this is particularly important - controversial. Other people love to chatter about stuff and this would only fuel the flames.
Don't follow anybody else. Or, if you must, make sure they are the kind of person who rarely checks out their accounts; the last thing you need is somebody trying to engage you in any form of communication. If this happens you must block them as quickly as you can... then delete your account, wait a few weeks and set up another account in a different name.
If you have an interesting byline or an intriguing profile with a funny picture this may also cause trouble. Tweeters are inveterately nosey people and will find themselves drawn to discover more, so don't give them anything to spark their collective curiosity. And your profile picture should really just be an egg.