The 25% that they take out initially is just the start. If you won $1M, you would be in the highest tax bracket. (Currently 35%) You will receive a 1099 form the following January or February stating the amount you won and how much was taken out for taxes. You will file this with your 1040 form along with your W-2's from work. The 25% actually covers your winnings up to about $300,000. After that your tax rate goes up. If you add your salary plus lottery winnings then subtract taxes taken out from your job and lottery proceeds, then you can roughly estimate how much more you will owe. Remember, that if you made that much money you will not be eligible to take all the deductions you may be used to taking if you made$50K or $75K, etc. You simply don't qualify for the deductions that millions of middle or lower class taxpayers get.
Figure on paying another 10% roughly on everything over $300,000 total income. If you are an average working class person with a medium or moderate income, you will owe another $70K give or take in this scenario.
You will NOT pay taxes on the original winnings after that first year when you file. You will however pay taxes on any interest or dividends earned in subsequent years with whatever principle you invested.
If you won $1M and they took out 25%, you would walk out of the lottery office with $750,000. Put $75,000 in a 3 mo, 6 mo, 1yr CD depending on how close it is to next April 15th. This should cover you and you still have $675,000 to work with.
With this much money, you should always consult a tax or estate attorney before you claim the ticket. You may be able to establish a trust, estate, or corporation and take advantage of tax laws to minimize how much the IRS gets.