Answer:
By entering before the deadline.
There are tons of contests out there and plenty of prizes to be won. Nothing is guaranteed, but there are things you can do to increase your odds.
First visit a sweepstakes site like SweepsAdvantage.com. The site is free to join. They gather up all the sweepstakes in one place so you don't have to spend to searching for them. The site also has great tools to keep track of what you have entered.
Seasoned sweepers will tell you that you need to be persistent to win. Set aside time each day to enter sweeps and stick to it. Most sweepers will also remind you that there is a certain amount of lag time in sweeping -don't expect to see a win right away. You could be filling out an entry form today for a contest that doesn't close for another three months.
Look for 'skill' contests since many other sweepers avoid them. If you take the trouble to enter the ones that require an essay or a photo or recipe, you'll be competing against fewer people.
Keep at it, and you will start winning. I did!