Blocking someone on Twitter is super-simple. As easy as clicking a single button. It IS in fact by clicking a single button. But there are some other things to know too.
Firstly, when you block someone it won't stop them logging out and looking at your profile, and seeing what you have written. You can only stop your updates from appearing on their "Friend's Updates" page. So don't just think by blocking someone gives you freedom to talk about them thinking they will never find out!
Secondly, they can still subscribe via RSS. They can have your latest posts send straight to their feed reader, or almost anywhere else.
Thirdly, they can just start following you in a different Twitter account.
Protect my Tweets If selected, only those you approve will receive your Tweets. Your future Tweets will not be available publicly. Tweets posted previously may still be publicly visible in some places.