"Shoe Shiners" are traditional and very popular all over the country, summer and winter, you can see them at each and every corner of the city and country.
Most of them have a specific area given by the Municipality, but besides, there are younger guys who carry their shoeshine boxes with them all thru the day to several spots of the city, especially to more touristic areas as like "Old City" or so ...
The traditional shoe shiners serve not just for shining your shoes, but besides also changing the color of your shoe, repair a broken part as like heel of the shoe, change the laces, fix the sole and many more ...
Eventhough you are a visitor / tourist in the city, feel free to leave your shoes with them in the morning and you can get back in the same evening as fixed like brandnew ... :)
Getting your shoes polished won't be a problem. On the major street you will find men that handle their antique tools with great enthousiasm. My advice is to pick out a seasoned shoe shiner and not get fooled by some passing charlatan (read: crook).
Little urchins starting to hustle their way up the economic ladder with a box of polishes, a rag, and a cheeky call - "Shoeshine mister?" One day, maybe they will become a taxi driver, with their own car.
It is the custom in Turkey, when entering a private house, to remove ones shoes. Having been in the Middle East previously, I know this, and even at home in England I don't wear shoes indoors. So, if you are staying with Turkish friends remember this, and take some slippers wth you.
Before entering a home, school or mosque in Turkey, it is customary for shoes to be removed. In a home visitors will be offered a pair of slippers to wear. Before entering a mosque, you will be given a plastic sack to carry your shoes in.
You can just seat and wait for your shoes to be cleaned. Of course in the streets it is not so luxurus!