After you file

Check Your E-File Status on this Secure TurboTax website
https://turbotax.intuit.com/efile/efile_status_lookup.jsp
- It will show the date you transmitted your return and if it was accepted or rejected.  
- Both your Federal and State will be listed separately if you filed both.
- It will tell you when you E-filed
- The electronic filing date

See the following TurboTax support article on checking your e-file status - https://ttlc.intuit.com/questions/1908859-how-do-i-look-up-the-status-of-my-e-filed-return

 

For the Feds:

http://www.irs.gov/Refunds/Where's-My-Refund-It's-Quick,-Easy,-and-Secure.

http://www.irs.gov/uac/When-Can-I-Expect-My-Refund%3F