The most important aspect of starting a business is that it must be something you enjoy. If the primary motive is money, but you don't enjoy it - it is a bad fit, and that is a sure formula for failure. However, if it is something you enjoy, you won't run out of enthusiasm. Your creative juices will flow, making your business a cut above the others, and increasing your chances for success.

List your interests. This will help you focus on businesses that will provide the greatest probability for success and eliminate possible failures.
List your skills. No one can be all things. If any aspect of business does not fit within your skill range these are the areas where you will need to get help.
Assess your personality. Are you a people person, or do you enjoy working alone? Do you love to serve others, or do you find people a pain? One ingredient that is sure to lead to failure is a reclusive or abrasive personality. Think about the people that you have met in business. Who were the ones that you wanted to give repeat business to?
Determine how much risk you can tolerate. Going into business can be scary; especially the first couple of years. Some businesses are scarier than others. If you lie awake nights wondering how large loans are going to be paid, or if you're going to be sued, maybe a business with less upfront capital or probability of lawsuit is more for you.
Determine how much time your business will require, and ask yourself if you are willing to commit the time. Many businesses require a huge time investment. Can you and your family tolerate a twelve or fourteen hour day schedule?
Take some classes. An excellent place to start is SCORE (Service Corps of Retired Executives), an organization that helps educate individuals considering starting a small business. After taking some SCORE classes some people are convinced that starting a small business is for them, while others are convinced it is not.
Have a plan. As the old saying goes, if you aim at nothing, you will hit it.
Set it up legally. Hire an attorney experienced in setting up businesses. He will guide you through the paper work and make sure things are done properly. A good attorney will not just do the paperwork and determine the business type (Inc, LLC, etc.) but will also advise you on common errors to avoid that can get you into trouble.

Find out about grants which may be available to help get your business started. The Princes Trust is a great starting point if you are aged between 14-30, and can offer lots of useful advice, as well as providing grants.

Keep in mind that the vast majority of new businesses fail. Always maintain a "plan B" just in case.
Don't do any monkey business!