If you're the type of teen who is heavily involved in extracurricular activities--things that take up a lot of your free time during the school year and leave little time for anything else--starting a seasonal business might be just the thing. Seasonal businesses are those that are only active during certain times of the year, such as during the summer or over the holidays. This way, in the "off season," you'll still have time to complete your other activities and schoolwork while maintaining your business only occasionally.
Since you said you want to start a business over the summer, first you'll want to decide on a business that will bring in profits over the summer and can lie dormant during the school year, easily resurrected once summer rolls around again. This can be as simple or complex as you like. Things like car washing, child care, lawn care and pet care are easy enough to get started and can be great ways to bring in extra money. But you can always take things a step further if you so desire. If you're tech-savvy, for instance, you could add a Web component to your lawn care business, making it easy for customers to get information about your service and book appointments. Create some business cards and other marketing materials that include your Web site address, and soon you'll have people from all over town visiting your Web site. This theory would work for virtually any kind of business you wanted to start.
You can create excitement for your service, too, by the fact that it's a seasonal business. If people know your service is top-notch and is only available for a limited time each year, they might be more eager to book appointments in advance--especially if you were to offer coupons and other special discounts. For instance, you could start a referral program whereby customers get a discount for each new customer they refer to you. And new customers could qualify for a special discount as well.
During your down time throughout the school year, don't totally ignore your business--take time now and then (perhaps over the holidays and other breaks) to clean up your Web site, and as it gets closer to summer, update those marketing materials and start putting the word out that your service will be available again soon. In time, you'll build a loyal clientele that will offer repeat business time and again.