Jenny Bay's post on this subject has a really great list of ways to find students, so I thought I'd just share my experience in moving to a new state in August.
First, my misconceptions about finding students. I had two groups in mind that I was sure would jump to join my studio: people at church (the first people I met here), and my immediate neighbors once we moved the piano out. Most people at church already had piano teachers so it took a bit of time for students who hadn't started any lessons before to come to me. As far as my neighbors, I think their children are just too young, at least right now. :)
On moving to our new city priority number one was to get permission. We live in student housing and they have certain rules about working in your apartment. Since we didn't have the piano yet I would be teaching in a common area, and therefore couldn't charge. This actually worked out really well. I've heard of people who offer a first free lesson or couple of lessons, but I did this out of necessity. I gained the trust of my first few students because I followed the rules. Those students have brought me referrals, but more on that later.
The students came to me after I put fliers up at all the bus stops. Our community has a lot of international students, so it would have been good for me to put an e-mail address on the flier for anyone who was nervous about speaking English on the phone to a stranger. I got my first five students with these fliers.
Since then I've gathered a total of 11 students: 2 students directly from other students, and four more who heard that I teach piano. Like Jenny Bay said, word of mouth is really the best way to find students--the parents are already more comfortable with you because they've heard good things from their friends and they can support each other as piano student parents, an under-appreciated but worthwhile pursuit.