Just make sure you save all your losers for the year. So when you do win you have a bag of losers you can write off the next year.
They'll give you a W2 (actually, a W-2G, but it acts the same), and you just figure your taxes like normal, with this W2 plus the one from your job
If you win less than $5k but more than $600, it's a little trickier. They give you a W2, but don't withhold anything. Which means you probably have to pay estimated taxes. But maybe not. Anyway, it's something to look out for.
TN both of the top two sentences are correct, your W-2G will look strange because it is probably smaller then the lottery ticket that you won on (make sure that you keep both of these for the end of the year). Bingo, you will still have to pay the federal taxes but say you win 4 grand, you will have to pay for that at the end of the year. Where you can make out is when they try to get their grand or so you can present them with the losing tickets like "gut" was talking about. As long as you have a grand worth of losers then you wont pay the taxes on it.