After starting the return hit the "Federal Taxes" tab at the top then the "Other Tax Situations" below it. File an Extension will be one of the options. It took me forever to find it. Hopes this helps.
If you need extra time and file an extension, it will waive failure-to-file penalties until October 18th. However, if you would have owed tax on April the 18th, the IRS will assess monthly late payment penalties and interest until you pay.
I recommend to extend your return with a TurboTax Extension and also pay your best guess of anything you may owe. If you overpay, it will be refunded. If you underpay, it will only calculate penalties on the part that was not paid.
The states vary according to their due dates and if you have to file an extension or if it is automatic. You can look it up on this TurboTax Help article and if a state extension needs to be filed, it should be an option at the bottom of the federal extension screen.
TurboTax has a tool called TaxCaster to give you an idea of your tax liability and/or refund. You can vary different items and see how that could impact your return. Click for TaxCaster