You should receive a W-2g with any wins over $1200 on high-odds bets paid in Nevada. What you signed was probably this form and you should have received copies of it on the spot. It's possible but not easy to get duplicates from the casino later.

You have to show all gross winnings on your tax return and can deduct your losses on schedule A up to the amount of winnings you report. The W2's also go to the IRS, so you should be sure you report (at least) the amount they show as gambling winnings on your return.

If you are subject to the Alternative Minimum Tax due to the amount of income in certain preferential categories, your deductions will be capped and you may not be able to deduct all your gambling losses. Good luck!