You do not file your form 1099-G with form 1096. Only the issuer of forms 1099-G does.
You can enter your form 1099-G for winnings by following these steps:
- In TurboTax, open your tax return
- Click on Federal, then on Wages & Income
- Locate the section Other Common Income and click on Show more
- Click Start next to Other 1099-G Income.