Your effective tax rate is the percentage you actually pay, and varies based on your total taxable income and your filing status (they tend to be better for a married couple.)
Your marginal tax rate refers to which tax bracket your income lands you in. Your total taxable income, including winnings, minus either the standard or itemized deductions is what you'll need to work out your tax rate. While your winnings are subject to both federal and state income tax, they're not payroll, so you won't have to worry about FICA. Your tax rate is determined by your income tax bracket and your annual gross income. Let's start with your federal income tax.