The game show will send you a 1099-MISC. The 1099-MISC would be entered under "Other Income" On the main screen, under Federal Taxes, select Wages & Income. On the next screen you can click "I'll Choose What I work on"
That will take you to the Income Summary screen. Scroll down and look for "1099-MISC and Other Common Income". Your prize money should be entered there. Note that the trip value may be overinflated.
You may wish to make estimated tax payments.
