You'll be able to file an extension thru TurboTax by clicking on the Federal Taxes tab, then Other Tax Situations, then scroll down to Other Tax Forms and select File An Extension.
The important thing to remember about extensions is that they only extend your time to file the return. If you owe money, then IRS and the states expect you to pay by the normal tax deadline -- there's no extension for paying.
Consequently, if you're filing an extension and you believe you'll owe, then you'll want to mail a check to IRS or the state. If you normally receive a refund, and you don't anticipate any change, then you don't need to send payment.
Some states will piggyback off the federal extension, so there's no additional state form to file. Other states require you to submit their own extension forms. TurboTax will walk you thru the state extension as well as the federal process.
If you're curious about your state, here's a list of extension requirements by state: https://www.irs.com/articles/state-tax-extension-information
https://www.irs.gov/pub/irs-pdf/f4868.pdf
