First, you need to get "Timeline." Gizmodo has step-by-step instructions here, but, in a nutshell, you just need to visit http://facebook.com/about/timeline and hit the big green button that says "Get Timeline."
Once you've upgraded and published your new profile, you'll find that there are two main avenues to messing with your friends on Timeline, both of which are time-honored Facebook traditions: posting annoying things to your friends' walls, and tagging your friends for embarrassing things. Timeline, however, has expanded your abilities to do these things. Remember that messing with your friends on Facebook is not, actually, "funny," nor is it intended to provoke laughter; it's merely a way to show your friends that you are thinking about them by being a dick.
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Messing With Your Friends by Posting to Their Timelines As always, a key way to irritate your friends is to post to their Facebook profiles; now, with the redesign, you can post to your friends' Timelines in any year you want. It's easy! Just click on the clock icon and select the date (you can be as general as a year or specific as a day) you want your post to appear.
Not only does this allow for whole new varieties of vaguely "funny" Facebook wall humor, it will also be really irritating to your friends if they can't figure out where your post is. I suggest you refer to yourself as "The Facebook Walker," an immortal being imbued with cosmic powers that allow you to traverse The Timeline. Note: Unfortunately, you can't post your friends' Timelines before they were born, so your hilarious "you've got to stop the JFK assassination!" joke, which you were the first to think of, for sure, will only work on people pushing 50.
How to Prevent This: Obviously, it's easy to remove the posts once they've been made, but to cut them off at the source requires a scorched-earth strategy: under "How You Connect" in "Privacy Settings," you can turn off your friends' ability to post to your Timeline.
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Messing With Your Friends by Tagging Them in Life Events This is my personal favorite new Timeline feature, and probably the best opportunity Facebook's provided for messing with your friends since the advent of "Places." You don't even need to visit someone else's profile to do it! Just start a new "Life Event" from your profile page and go crazy.
Did you have your First Kiss with your college roommate? Did you start New Eating Habits with a coworker? (I did, apparently, or so I was informed yesterday by Facebook.) Add a photo! Add a date! Add a place! The Timeline is your oyster! Note: by messing with your friends by tagging them in weird life events on your own timeline, you are, in effect, messing with yourself. Consider yourself warned.
How to Prevent This: Unfortunately for the messers, but fortunately for the messees, this is pretty easy to fix. If you edit "How Tags Work" under your Privacy Settings, you can turn "Timeline Review" on—giving you the ability to approve (or reject) any attempts by friends to tag you in their life changes.