Facebook and Twitter are common candidates for organizing a popular protest--so much so that the less-discerning reader might think that Egypt's next president will be Mark Zuckerberg and the Fail Whale the symbol of the former Tunisian president. That's because if you have a compelling message, those two services are possibly the easiest ways to mass-distribute that message to your peers, who will then share it with their peers, and so on.
Take Facebook, for example. The days where the Facebook Groups were dominated by I Will Go Out Of My Way To Step On That Crunchy-Looking Leaf are over. Instead, Facebook Pages can be used as a nexus for a mass movement--see Google's Head of Marketing in the Middle East, Wael Ghonim, whose contribution to the recent Egypt revolution started with a Facebook Page for Mohamed El-Baradei and another page called We Are All Khaled Saeed. As it turned out, those two pages served as easily-accessible forums for 400,000 people to voice their unrest.
Facebook is great for sharing links, photos, videos, and news with your friends, family, and colleagues--whether it's about your new baby or your new political movement. While text-driven discussion pages serve an important purpose, you'll be better able to propagate your message if you have readily-shared photos and video on hand. A carefully-chosen photograph or video of an innocent person being beaten by the ruling party, for example, can quickly boost revolutionary fervor to a fever pitch.
Post that video on your Facebook Page, and all people have to do is click the Share button to send it to their own networks. Best of all, Facebook defaults to including the name and link to the original Page or user that shared the link, so anyone who sees your link on their friends' Facebook accounts can easily check out your Page and join the movement.
Up-to-the-minute live coverage doesn't work quite so well, however, because the Facebook default view doesn't necessarily show posts in a chronological order. For that, you'll have to use Twitter.
Twitter was briefly a media darling for its (likely overstated) role in the 2009 Iran election protests. Where Facebook is excellent for sharing longer messages among your personal and professional social networks, Twitter is better used for sharing links and up-to-the-minute news from whatever tech you happen to have handy. Also, since Twitter isn't necessarily linked to your real name, you can be a bit more anonymous on Twitter than you can on Facebook--which could be crucial, whether you're an organizer or a foot soldier.