Do I need to claim the money that I receive for giving piano lessons for a few friends children, not technically a busines?

You are required to report all income on your return. The income is considered self employment income. As self-employed, it's likely you need to fill out an IRS Schedule C to report your income and expenses. 

Where do I enter Schedule C?

You can deduct eligible business expenses to pay fewer taxes. These expenses must be common for your type of business and also necessary for your operations.

For more information, check:

What self-employed expenses can I deduct?