I would think all you need to do is sign in??? I use my home computer, work, friends, etc. and never have any trouble signing in. Or am I misunderstanding your question?
When you block a person, they can no longer invite you to a private message or post to your profile wall. Replies and comments they make will be collapsed/hidden by default. Finally, you'll never receive email notifications about content they create or likes they designate for your content.
Note: if you proceed, you will no longer be following .