You should make a "good faith effort" to ascertain the Fair Market Value (FMV) of the prize if you didn't receive a 1099-MISC nor any other correspondence from the prize company. Do you know what a similar item may be worth? E.g., a 32" TV is about $150 at a big-box store.
You would enter the amount as Other Taxable Income which will then show up on line 21 of your Form 1040.
To enter/edit prize money (not on a 1099-MISC):
1. Open your return (or continue if open).
2. Click on “Take me to my return” button.
3. Click on Federal tab (left-hand side of screen).
4. Click in Wages and Income (near top of screen)
5. Scroll down to Less Common Income.
6. Click on Start next to Miscellaneous Income.
7. Click on Other reportable income (all the way at the bottom as you scroll down); Click “Yes”.
8. Enter “Description” and “Amount”.
Please see attached screenshot below.