I don't have any students at all, but I've been in the middle of the classical music scene in my city, having a degree, and many friends and colleagues who started teaching. I still see new studios with familiar acquaintances involved pop up all the time so it's clearly in demand.
Most of these people just do guerrilla poster marketing when they get started. Normal printing paper with information and your studios website, phone number, email, taped up here and there in your area.
If you have a budget you can do facebook marketing targeting people in your area. It's a long time since I did facebook marketing but as far as I recall you can get enough views and clicks out of 200 dollars.
Apart from that you can put the word out among your colleagues that you are looking for students and sometimes get referrals that way.
Several people I know primarily targetted the rich areas of town. Rich people are willing to pay more and piano lessons are valued in these circles.