Have you been to Subway? Imagine that system but with gyros and Greek salads. You go in and pick if you want white pita, wheat pitas, or a salad. Then you go and pick your meat, tzaki sauce (they have 2 choices yogurt or sour cream based), and veggies.
There will be a line here at lunch, do NOT let that intimidate you, it typically moves very quickly and the staff is good at keeping it moving. They also have alot of outdoor seating right there in Market square. I highly reccomend grabbing your gyro and sitting outside on a nice summer day and enjoy the ambiance of Market square without the need to fight for a table and enjoying a great gyro.