Ever wondered what it’s like to be invisible? That’s what happens when you Block someone on Facebook. They become invisible to you and you become invisible to them. The blocked person can’t search and find you or vice versa. It is as if neither of you exist on Facebook...at least to one another. There are several ways to Block someone.
The easiest way is to Block the person from their Profile Page. Scroll down the page and at the bottom of the sidebar (on the left hand side), there is a link to Report/Block this Person. Click it with your cursor.

A pop-up box will appear with the title, Report and/or Block this Person. Check the box that says Block this person and press the Submit button. Voila! You have officially Blocked someone (and no, they are not notified).

Another way to Block a person is found through your Privacy Settings found on your Profile or Home Page.

On the Choose Your Privacy Settings Page, click on the Edit your lists link under the heading Block Lists (in the center bottom of the page).

In the Block users section, you can choose to enter the person’s first, last or full name in the Name box or their email in the Email box and press the Block This User button. A pop-up box will appear with possible people who meet the criteria you typed in. Once you find the right person, press the Block button and they are officially added to your Block List.

Notice that they appear in a bulleted list of names of people you have Blocked. If you ever want to unblock them, press the Unblock link and they will no longer be invisible to one another on Facebook. If you want to become Facebook Friends with the person, you will need to send them a Friend Request.
source: The Facebooking Couple (K. Jason & Kelli Krafsky), authors of Facebook and Your Marriage at FacebookAndYourMarriage.com.
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