I'm a retired teacher, with $40,000 annual income. As a composer, I am now making about $6,000 a year. Should I start a business or just report this as extra income?

You should report this as self employed income on Schedule C.  

This will allow you to deduct any expense(s) associated with your income.  You might be surprised on how much mileage and other expense will reduce your taxable income.

However, be aware you’ll owe tax that you never had to pay as an employee. The self-employment tax (officially known as the SECA tax for Self-Employment Contributions Act tax) is the self-employed person's version of the FICA (Federal Insurance Contributions Act) tax paid by employers and employees for Social Security and Medicare, and it's due on your net earnings from self-employment.

You report your earnings for Social Security when you file your federal income tax return. If your net earnings are $400 or more in a year, you must report your earnings on Schedule SE, in addition to the other tax forms you must file.

-follow these links for more information-

The Self-Employment Tax - TurboTax Tax Tips & Videos

Tips to Reduce Self-Employment Taxes - TurboTax Tax Tips ...