if you're just starting out, naturally you're not going to have a whole lot of money.. best way to advertise your school is not to worry too much about advertising in newspapers etc. it's expensive and only runs once, and most people are naturally programmed to ignore ads in the paper, unless they're huge and ad rates for big ads are incredible, don't do it until you get a good income base..
go for flyers - go for a black and white flyer, either 1/2 a page or 4 to a page. keep it simple - what you teach, where you're located, how to contact you, great for all ages(if applicable) the bottom price you offer per month, and maybe a cool graphic. print tons, cut and pass them out at grocery, department stores and colleges or after schools get out.. flyer cars at your local mall or department stores, during parades walk down the sidewalk and pass them out..
print larger ones and stick them on every billboard in your town...
free demos at local fairs are great too, if your town does octoberfest/july 4th/arts festivals etc.. offer to do a free demo to the coordinator, it takes up time in between band set ups and is entertaining for spectators, and possible money maker for you..
it's added exposure and gives people a demo of what they might expect if they come to your school.. also this is another great opportunity to pass out info on your school..
this is the best route to go if you're just starting out.. hope this helps!
~*good luck*~