I'm a junior academic born and still living in Istanbul, and teaching assistant to a popular historian at my university. So while I'm not precisely qualified to answer your question, I've consulted some of my books to fill in the gaps.

I guess it's best to begin in medias res, and we can join Michael VII's general Alexius Strategopulos when he rides to Selymbria (the modern Silivri) on the coast of Marmara with a small army for a reconnaissance mission. He sees to his surprise that the Latin garrison is absent, as the Venetians want to take Daphnusia (the modern Kefken Adasi), which controls the entrance to the Bosphorus from the Black Sea. Alexius also locates a postern gate in the walls which some men could easily pass through. The city is basically there for the taking.

That night a detachment enters the city and throws the guards from the ramparts. Then they quietly open one of the gates. On 25th July 1261, just when the sun rises, the Byzantine army sets foot in the city.

The Latin Emperor Baldwin II, asleep in the Blachernae Palace, woke up to the sound of fighting. He left in such a hurry that he left his crown and sceptre behind. He made his way to the Bucoleon (near today's Kumkapi on the Golden Horn) and escaped on a Venetian merchantman to Euboea. Meanwhile Alexius ordered his men to set fire to the entire Venetian quarter, so the soldiers coming back from Daphnusia to find their houses destroyed and their terrified families waiting for them would have no choice but to leave.

There were thirty Venetian ships waiting, and they also sailed for Euboea. But sources say that they also left in a hurry, as they didn't think of taking provisions. Many of the refugees died of hunger before reaching their destination. The deposed Latin emperor embarked upon a series of intrigues to take the city back, but he would never see it again.

The Byzantine Emperor Michael VII was asleep in Meteorium in Asia Minor when his sister woke him up and told him the news. (The two sleeping emperors make a very nice pair, very poetic.) He didn't believe her and she had to show him Baldwin's abandoned regalia. He began preparations and on 15th August 1261 he made his entry to his recaptured capital by the Golden Horn. He was preceded by the great icon of the Virgin Hodegetria - "Virgin who points the way", believed to be painted by St Luke himself. He completed the ceremonial entry at Hagia Sophia, where a second coronation ceremony was performed by Patriarch Arsenius. Michael VII was crowned basileus, and the Latin rule was over.