The IRS began to accept e-files today. It may take a few days before they get to all the e-files that are piled up on the servers. Watch your emails.
When you e-file your federal return you will receive two emails from TurboTax. The first one will say that your return was submitted. The second email will tell you if your federal return was accepted or rejected. If you e-filed a state return, there will be a third email to tell you if the state accepted or rejected your state return.