Your initial lottery win is considered to be a "prize" under the tax code, just as though you had won a contest; the tax on your win is levied at the short-term rate, which is essentially the same as paying personal income tax (35%) in your new, higher bracket. However, once your money is properly invested, you will be able to take advantage of long-term capital gains benefits for your second and subsequent years. In order to qualify for the long-term capital gains rate, you must hold your investment for at least 366 days.
Some say you can write off a certain amount of any losing tickets you've managed to accumulate during the same year, but I've spoken with others who say they were denied that deduction on a major win (I believe the maximum is $3,000.00, but this might have changed by now; talk to an expert).
Any Certified Public Accountant can give you more details, and it won't cost anything unless you decide to hire him to look after your nest egg. I would strongly recommend taking the time to speak with a CPA or a qualified financial adviser before you win the jackpot, as there are specific exceptions to these rules that can bite you when you're not looking, such as the AMT, or Alternative Minimum Tax.
Here's a link to an IRS page that does a decent job of explaining it, but you should still make an appointment to speak with an expert (it's what they do for a living):
http://www.irs.gov/taxtopics/tc409.html
Also check out Fool.com (the Motley Fool's website) for more insights:
http://www.fool.com/taxes/2001/taxes010105.htm This page hasn't been updated since 2001, but there's still a lot of useful information here.
Hope this helps, and good luck!