Where do I find out how much I owe for my state taxes? TurboTax doesn't seem to know the amount or where to find it.?

You will be able to see the amount of you federal and state tax refund or liability on the top of your screen as you enter your income and expenses.  

Please be aware, the amounts on the top of your screen are not final until you are ready to file your tax return.  Every item you input will change your overall tax total and will change your refund or balance due accordingly.  

I had already filed.my taxes. And it never said how much I owe. I am supposed to get some back from Federal but don't know about the state. I was just wondering how to find it after I have filed.

To get a copy of your 2020 tax return that you filed this year (if it has been accepted), you may log back in to your account and select Download/print return. Once you do this, you will be able to take note of your exact refund amounts for both federal and state. Please see the screenshot below for an example of how this should look :

Screenshot