After you file

"Accepted" means the IRS has agreed it meets the format for a properly efiled return and that processing can begin.

You can monitor the status of your Federal refund at this IRS page below.  If you efiled, wait 24 hours after acceptance before trying this tool, or it may not find it.
http://www.irs.gov/Refunds

No one can know exactly when your funds will be deposited.  There are too many variables including differences in bank processing times once the IRS sends the funds.

The IRS says 9 out of 10 filers who efile and choose direct deposit will get their refunds within 21 days.  You can monitor it with the IRS tool mentioned below.  Some returns take longer for additional processing due to specific items in the return.  Some are pulled at random for more thorough investigation.

Also, if you have EIC (earned income credit, aka EITC) or ACTC (additional child tax credit), the IRS will not start releasing those refunds until February 15.  That means people with those types of credits may not start receiving their refunds until around February 27.

NOTE:  If you chose to pay any TurboTax fees out of your Federal refund, that is another link in the chain, since your funds go first from the IRS to an intermediary bank where the fees are subtracted.  Then that intermediary bank sends the rest of the funds to your bank in a second direct deposit.