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You think you know what Arab rage looks like: wild-eyed young men shouting bellicose verses from the Koran as they hurl themselves against authority, armed with anything from rocks to bomb vests. So who were these impostors gathered in Cairo's Tahrir (Liberation) Square to call for the resignation of President Hosni Mubarak? They were smiling and laughing, waving witty banners, organizing spontaneous soccer tournaments and thrusting cigarettes and flowers into the hands of Mubarak's soldiers. They may have turned U.S. policy in the Middle East on its head, but even the American President was moved to praise the people who humbled a staunch Washington ally. Those "who believe in the inevitability of human freedom," Obama said, would be inspired by "the passion and the dignity that has been demonstrated by the people of Egypt."

Those qualities helped undermine one of the Middle East's most durable dictatorships, as well as any number of stereotypes associated with the Arab street. The careful civility energized many thousands of Egyptians who had never marched in protest in their lives to take their families to the city center to assert their claims to freedom. It even seemed to embolden the American President, who like his predecessors has celebrated the prospect of Arab democracy while supporting the dictators who suppress it. Speaking shortly after Mubarak's offer to step down ahead of general elections in the fall, Obama cited the maturity and civic-mindedness of the protesters as reasons for hope that Egypt would deal successfully with difficult questions in the weeks to come.

But the protests brought other scenes, more familiar and more ominous. Power abhors a vacuum, and on Feb. 2, when armed pro-Mubarak forces — as faithful to the stereotype as to the President — confronted the protesters with rocks and machetes and Molotov cocktails, it reminded the watching world that historic change seldom comes gently: this is no velvet revolution. The rearguard action by Mubarak's thugs felt very much like the final spasms of a dictatorship that won't go quietly. Provoked by the brutal counterattack, the protesters abandoned their peaceful posture and fought back. The square became a battleground between pro- and anti-Mubarak groups, with the military unable or unwilling to intervene.

The battles may continue, but it seems clear that the revolution is won: that Mubarak will go is no longer in doubt. And that's because hundreds of thousands of people across Egypt joined an uprising that in its first exhilarating week felt like none other in the history of the Middle East. So who were the people who pulled it off? Here's a guide:

The Organizers
Most Egyptians who joined anti-Mubarak demonstrations in the week leading up to the Feb. 1 "march of millions" in Tahrir Square say their participation was spontaneous. Many had never attended a political rally before Jan. 25, the first day of protests. But the date and location of that demonstration were hardly impromptu. The event had been planned weeks in advance by a loose coalition of activists who used social-media sites to commemorate Khaled Said, a young Egyptian allegedly beaten to death by police last summer. The cause was joined by some political groups, including the April 6 Youth Movement, named after an industrial strike in 2008, and the Ghad (Tomorrow) Party of former presidential candidate Ayman Nour.

Shadi Taha, 32, a Ghad Party member, says he and fellow organizers chose the date for a reason: Jan. 25 was Police Day, perfect for drawing attention to atrocities committed by a police force renowned for its brutality. A protest at Tahrir Square, the site of past demonstrations like the bread riots in the late 1970s, would be a good way to gain attention from the news media. In the early planning, Taha and his fellow activists envisioned a gathering of about 200 protesters. Then, two weeks before the demonstration, Egyptians, like Arabs everywhere, were mesmerized by the popular uprising in Tunisia. They watched the Jasmine Revolution unfold on satellite TV and saw Zine el Abidine Ben Ali, Tunisia's ruler of more than two decades, flee. "That gave us hope that this might happen in Egypt as well," says Taha.

Galvanized, the activists started going door to door, passing out flyers about the Jan. 25 protest. They put up Facebook pages and posted on Twitter. Nour spoke out against the regime in a YouTube video. Others exhausted their thumbs sending out text messages. "Tell your friends," the messages read. "Look at what is happening in Tunisia. This is how people change their country." They even dialed random numbers in the hope that the exhortations to demonstrate would fall on sympathetic ears.

For all that effort, Taha says that in his wildest dreams, he would not have expected to see 5,000 people in Tahrir Square on Jan. 25. He counted more than 10,000. The turnout also caught the Mubarak regime by surprise: police were unable to prevent the crowd from gathering and had to fire tear gas to get it to disperse. By Egyptian standards, the demonstration was a huge success, and it inspired other people to join. "When the older people saw the younger people go out in the street, they started to come out too," says Amer Ali, a lead organizer in April 6. Spontaneous demonstrations began to break out elsewhere.

But Egyptians, long cowed by the heavy hand of Mubarak's police and intelligence forces, needed a crash course in protest. Activists used websites and text messages to pass around how-tos, some borrowed from Tunisian bloggers: Coca-Cola, they said, was good for washing tear gas from one's eyes. The pro-opposition Al-Masry al-Youm newspaper published tips on staying safe in a demonstration: wear comfortable clothes, tie long hair into a bun, bring water. And this: "Be careful whom you're talking to [because] some 'protesters' may be plainclothes police and may arrest you."

The Protesters
The advice was aimed at people like Ahmed Shahawi. The unemployed engineer had been drawn to the Jan. 25 demonstration, and he urged his 122 Facebook friends to join him. It was his first taste of political protest — and of tear gas. Afterward, he updated his status: "I'm safe, guys. I'm going back to the Square tomorrow." He was hooked.

Shahawi's Facebook alias is Nicholas Urfe, from the character in John Fowles' The Magus who thought he knew everything but didn't. For Shahawi, the Tunisian revolution was an education. Egyptians his age, born right around the time Mubarak became President, have never known any other leader and never believed change was possible, he says. "Tunisians gave us a live example that, yes, you can change the system, and they gave us the courage to do it."

When the government blocked the Internet on Jan. 27, Shahawi needed to find another way to communicate with people who felt the way he did. "I got in my brother's car and said, 'Quick, let's go downtown.'" In retrospect, he believes the government's decision to shut down the Internet backfired. "When you block the Internet, you are asking people to come on the streets," he says, "and anything can happen."

Forced to abandon his virtual world for the real thing, Shahawi found himself drawn into a new community. On Feb. 1, the day of the million-person march, he and 50 other men hauled bags of trash from the city center and piled them into a makeshift dump they'd created. Shahawi said the demonstrations had fostered a sense of unity among people and a stronger civic sense. "This is the first time we see all the Egyptian people all together like this," he said.

That sense of purpose was also apparent in neighborhoods far from the square, where people were left to fend for themselves after police withdrew following the initial protests. Residents formed spontaneous watch groups to guard homes and shops against looters. After vandals broke into the Egyptian Museum, volunteer guards joined forces with the military to make sure they didn't return.

Grownup Rebels
If Egypt's rebels behaved like responsible grownups, it's because so many of them actually are. Thirty-somethings like Taha and Shahawi, rather than hotheaded university students, have organized and led the protests. The government employs a network of informants on campus to ensure that students stay apolitical, so it's usually after their university years, when graduates have endured long unemployment — and its cultural consequence, the inability to marry — that some drift into politics.

The revolution also benefited from a cadre of political activists who had learned the ropes from campaigning ahead of parliamentary elections late last year. When the vote was blatantly manipulated to give Mubarak's National Democratic Party over 80% of the seats in the People's Assembly, it left opposition activists bitter — and united in their desire for revenge.

That unity helped opposition groups coalesce briefly around Mohamed ElBaradei, the 2005 Nobel Peace Prize winner and former head of the U.N.'s nuclear watchdog group. For Western observers, this allayed concerns that Mubarak's exit would leave Egypt in the hands of the Muslim Brotherhood. The Islamist group, which rarely goes along with secular parties, hung back and let them take the lead. The Brotherhood seems to have made the shrewd calculation that the revolution would attract more participants if it wasn't overtly religious. Abdel Mineem Abu al-Fotouh, a member of the Brotherhood's powerful political bureau, told Time it would not seek power. "[We] will not have a candidate after Mubarak, and we don't want to replace the regime. This is not our agenda," he said. The Islamists' goal, at least for the moment, is to cultivate a moderate, democratic image in the eyes of fellow Egyptians as much as with the West. That's another Arab stereotype turned upside down.

By the end of Feb. 2, the thinning crowds of protesters in Tahrir Square were sullen and somber, a far cry from the ebullience of the previous day. There was no more talk of soccer matches, no praise for the military's studied neutrality. But one emotion did survive the bloody denouement: a determination to keep the revolution alive until the despot was gone. "He can't kill us all," said Mostafa Higazy, an engineering professor. "This is an uprising for the freedom and dignity and justice that he took away from us." The revolution, said many in the square, had brought them within a whisker of victory. This was no time to quit.

— With reporting by Abigail Hauslohner, Rania Abouzeid and Vivienne Walt / Cairo and Aryn Baker / Beirut

• Bobby Ghosh