Obtain a copy of the latest U.S. News & World Report "Best Colleges" issue. This information can also be found online. Their research ranks engineering programs across the country at all degree levels. Schools are scored based on a number of categories, and information is available concerning admissions, academics, and cost.
Decide how important location is to you. If you are from the Midwest, and you definitely want to remain close to home, then limit your search to the Midwest region. If you want to study at the best school in the country, then don't limit your search geographically.
Take an in-depth inventory of your financial situation. If you will be paying for college by yourself, then a university that charges $40,000 for tuition may be quite a struggle for your mind and your bank account.
Choose a major. Although this isn't 100% necessary upon admittance into most schools, it could serve as a beacon in your search for the perfect engineering school. Some schools are well known for certain branches of their engineering programs. If you are drawn to that prestige, you may be drawn to that school. It is fairly easy to change your major after starting classes, provided you aren't near the completion of your degree.
Go on campus visits. Brochures and websites may lead you to believe that you have found the perfect engineering school, but there is no better way to lock that decision in than to go on a campus visit. The visit can be the deal breaker in your decision. The student body make-up and the aesthetics of the campus (good or bad) will stick with you after just one day as a visitor.