When i was about to finish highschool i decided that i was going to tutor for some extra pocket money. I had only planned to tutor about 2-3 kids as a side job. The first person i began tutoring was a friend who was a year younger than me. She was doing chemistry so i tutoried her in that.
The next person i began tutoring was somebody who my mum found, who needed extra help with maths, physics and chemistry, so i began tutoring him twice a week. And then from there it went crazy; word of mouth got around and ever since ive had quite a few people approach me for tutoring. At the moment ive got about 12-13 people i tutor each week, and ive had to do no advertising at all. It was 100% word of mouth. I had never planned to get so big with it, so now its pretty much my main form of income while i am at uni
There are a few websites around that allow you to post your name as a tutor and then let other people contact you. Ive never tried these so i dont know how effective they are. I guess it depends where you live, but you may need a "working with children" licence. I never had one to begin with (even though i probably should have), but the highschool i went to contacted me to hire me to do small group tutoring sessions, and so for legal reasons i was made to get one.
If you can, you could perhaps approach some of the teachers in the school and give them your phone number so that they can give it to any students who are seeking a tutor. I know that a few of my highschool teachers were approached by their students seeking a tutor, so some people were able to get in contact with me through my old teachers.