The easiest way (which is also the way that worked the best for me) involves using AdBlock Plus on Firefox or Chrome, and adding the following custom filters in the extension's preferences.
www.facebook.com##[id="pagelet_rhc_ticker"]
www.facebook.com##[id="pagelet_ticker"]
Then, refresh Facebook and you should be in business (that is, the news ticker should be gone).
If you have Chrome, you can also install Unannoying Facebook, which gets rid of the news feed as well as the pinned bar on top. Or, if you have the Better Facebook extension, you can paste this into the CSS options under Advanced Options Mode.
/* Hide Facebook live ticker */
.ticker_stream { display:none !important; }
We'll spare you the Xzibit jokes and just be glad that the stupid news feed is gone.