Marketing: Door to Door or Facebook Galore
Back when I was a kid, I used to rake leaves for extra money. I had what I considered the perfect strategy at the time. I would look for the house on the street with the most leaves on their lawn, and then I would offer to rake those leaves for a few dollars. Basically, the idea was that there was obviously a need for my services, and I didn't want anyone to turn me down because of the price. I was 12, and I figured some money was better than no money. My strategy was good, but I should have asked for more money. But that was before the Internet (I know, I'm old), and no one was writing articles about tips on a lawn mowing business for teens.
If you go door to door to try and drum up business, target the lawns that look unkempt. People who already have a lawn service might be willing to switch to you if you offered them a better price, but they may already be happy with their gardener. If you target the people who obviously need your services, you are more likely to pick up some business, especially if you catch a guy like me who wants to spend his Saturday playing video games, not mowing the lawn.
If you have access to a truck, consider marketing on Facebook - social media marketing is easy and, best of all, free. You can even ask your parents to make a post to their wall about your lawn services. Chances are, your parents' friends will be more than willing to help. It's free advertising, and you can make all of the arrangements from the comfort of your home or cell phone.