The Ottoman MO at the time was to take a Byzantine city without a siege if possible. Thus, it was customary to send a letter demanding the city be open to the army and some places did comply. However, if this "request" was refused and the town did fall, the victorious army would loot and pillage for three days. After 54 days of digging, blowing stuff up with giant cannons, dragging a fleet across land, starving the city, etc., etc., the forces of Mehmed II breached the walls and the army looted and pillaged.

From Kritovoulous' History of Mehmed the Conquerer, written about a decade after the event: "And the desecrating and plundering and robbing of the churches -- how can one describe it in words?...The last resting-places of the blessed men of old were opened, and their remains were taken out and disgracefully torn to pieces, even to shreds, and made the sport of the wind while others were thrown on the streets"

From Nicolo Barbaro, a Venetian who had fought against the Ottomans at the battle: The invading force "went rushing about the city, and anyone they found they put to the scimitar, women and men, old and young, of any condition. This butchery lasted from sunrise, when the Turks entered the city, until midday, and anyone whom they found was put to the scimitar in their rage. Those of our merchants who escaped hid themselves in underground places, and when the first mad slaughter was over, they were found by the Turks and were all taken and sold as slaves."

From George Sphrantzes, a Byzantine courtier turned monk who saw the battle firsthand: "On the third day after the fall of our city, the Sultan celebrated his victory with a great, joyful triumph. He issued a proclamation: the citizens of all ages who had managed to escape detection were to leave their hiding places throughout the city and come out into the open, as they to were to remain free and no question would be asked. He further declared the restoration of houses and property to those who had abandoned our city before the siege, if they returned home, they would be treated according to their rank and religion, as if nothing had changed."

(I realize that I've quoted mainly from people who lost and stood to lose much from the event. If you want an account from someone of the winning side, so to speak, look up Tursun Beg's "History of the Mehmed the Conqueror" I can't seem to find an excerpt in the sources available to me right now.)

After the three days of looting, slave-taking, (and, yes, some reported rapes), Mehmed set about restoring order and the city itself. Constantinople had seen a drop in population as it went from being a great capital of a great empire to functionally a city-state with control only of its hinterland. There was a great deal of architectural rebuilding to the city to clearly signal who was now in charge of the second Rome. Most famously, the Hagia Sofia was converted to a mosque, mihrab, minarets, and all (although some of the mosaics depicting human forms would not be covered up until a few centuries later). In all, something like six of the city's churches were converted to mosques. The city's population was also bolstered by groups relocated from Anatolia. To quote Finkel, "people of all religions were attracted by favorable taxation and the promise of a better life. When taxes and other inducements proved inadequate attractions the Ottomans had no qualms about uprooting and resettling their subjects if it suited their economic or political aims." For the Muslim newcomers, the sultan encouraged his court to build up new neighborhoods and he and his family funded numerous charitable and commercial buildings like baths, markets, and caravansarays. Mehmed II also took to repair the walls damaged during the siege and building bridges.

Source: Osman's Dream by Caroline Finkel.