Start in Istanbul's Aya Sofya Square. The building is open Tuesday to Sunday from 9 a.m. to 7:30 p.m., though the upper gallery closes at 7 p.m.. Admission is charged. The ticket office is on the southwest corner of the complex. Go through security and into the courtyard. In the upper left corner, you'll see a café and in the upper right, the ruins of one of the previous churches that occupied this site. Hard to the right is the back end of the gift shop. In the middle of the eastern side of the courtyard is the main entrance. Once you enter the building, cross the outer narthex and go into the inner narthex to the central Imperial Entrance, over which you'll see the mosaic of Christ Pantocrator.
Enter the nave, taking note of the Islamic medallions hanging from the ceiling and of course, the dome, with its many gilded mosaic tiles. Turn left and just past the alabaster urn is the "weeping" or "miracle" column. Legend has it that if you have an ailment and stick your finger into the hole in the column and the finger's wet when it comes out, you'll be healed. Of course, after all these centuries, the hole's probably about as hygienic as the Blarney Stone.
Work your way around the north gallery past the raised marble loge used by the Sultan during prayers, over to the apse on the east side. Here you'll see a mosaic of the Virgin Mary and the Child Jesus, the mihrab, or niche facing Mecca, and the minbar, the pulpit from which Islamic imams gave their Friday sermons. Just south of this are mosaics depicting Christ as a child and adult, the Virgin Mary and various Byzantine emperors and empresses.
Continue into the nave. On the south side under the great dome, you'll see the Omphalion, a circle of marble on the floor. It was on this spot that Byzantine emperors were crowned. From here, you have a good view of the mosaic of St. John Chrysostom on the north side of the nave. Move along to the south gallery to see the library of Sultan Mehmet I.
Head back to the inner narthex, go up to the north end and take the ramp up to the galleries, which were used by the Empress of Byzantium and her retinue. From here you can get much better views of the mosaics, many of which are only now being restored, having been painted over when the building was a mosque. Go back downstairs and down the inner narthex and stop off at the gift shop to the right. Leave through the Vestibule of Warriors. To the left is the former baptistery, which contains the tombs of two sultans, while to the right is a gazebo-like structure, under which is the former fountain used by Muslims for their ablutions prior to prayers. The tombs of several sultans are to the south of the main building.