I'm getting a refund this year but still owe from last year. Can my refund be applied to what I owe from last year's taxes? If so, how does this work?

Thank you! What about CA State? I owe them from last year too.

TurboTax gives you an estimated date for receiving your refund based on a 21 day average from your date of acceptance, but it can take longer.
Once your return has been accepted by the IRS, only the IRS has any control.  TurboTax does not receive any updates from the IRS.
To track your Federal refund:   
<a rel="nofollow" target="_blank" href="https://www.irs.gov/refunds">https://www.irs.gov/refunds</a>
To track your state refund:    
<a rel="nofollow" target="_blank" href="https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund">https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund</a>
On the IRS site you are also offered the use of an app called IRS2Go
<a rel="nofollow" target="_blank" href="https://ttlc.intuit.com/questions/1901548-why-do-some-refunds-take-longer-than-others">https://ttlc.intuit.com/questions/1901548-why-do-some-refunds-take-longer-than-others</a>
If you chose to have your TurboTax fees deducted from your federal refund, that will take some extra time.