I teach guitar/bass/mandolin from home full time and have for a few years.
Though it only works if you're good, nothing beats word-of-mouth for getting students, but you have to START more aggressively than that by getting the word out yourself locally. Ads in music stores, elementary schools, high schools, universities, colleges, church halls, libraries, gyms, grocery stores...anywhere that potential pickers or their parents go. Don't overlook cool cafes and rock oriented clothing stores and the like. Newspaper ads are expensive if you want graphic visibility so save your receipts for tax time. Ask to put an insert in school newsletters. Speak with other local instructors to see if they can off-load some of their waiting list. Be visible and vocal about your service at gigs, jams, sessions, etc. Put your professional looking business card in people's hands. Once you have a small core number of students, word-of-mouth should sustain your business. I do not advertise, at least I haven't done more than a poster in the local mom'n'pop music shop for years. Word-of-mouth does it all...I haven't had fewer than 50 students for a few years.
Know your theory, have firm lesson plans, read and teach reading, don't go slack on technique, have a good space, lighting, equipment, be punctual.
One pet peeve of mine are teachers who start up their business for occassional pocket coin rather than long term investment in learning continuity for dedicated students. This can be a huge disappointment for students who are dumped just because the teacher has changed his mind, found other work, or is too lazy to do the work involved in the job. Sure, it creates more job security for me, but there are lots of folks who just don't get lessons when they need or want them most...if at all.
I'd be happy to answer specific questions about payment, scheduling, books and whatever else if you're interested.
Peace, Mooh.