I filed and submitted my tax return and chose to have it mailed Will it automatically be sent to the address that I gave them or is there something else I need to do?

If you chose to have the tax refund mailed to you, the IRS will mail the refund to the address you entered on your federal tax return.  There is nothing more that you need to do.

After you submit it you should come back and check if it got Accepted here

https://turbotax.intuit.com/tax-tools/efile-status-lookup/   

When you efile you get back 2 emails.  The first email only confirms the transmission.  The second email says if the IRS (or state) Accepted or Rejected your efile.

When you log into your account you should also see the status and if it was Accepted or Rejected, Started, Printed, Ready to Mail, etc.  What does it say?