Preparation
Successful Jeopardy! players have a lot of knowledge on a wide variety of topics. To gain additional knowledge, they study and cram facts before even trying out to be a contestant. Write down the categories from one week's shows. Note which categories tend to appear often, such as "literature." Study most from the areas you tend to know the least.
Favorite Topics
Former contestants have noticed that certain topics tend to come up again and again, though the questions themselves are different. Take their advice and study literature --- especially Shakespeare --- U.S. presidents and "Jaws."
The Buzzer
Every Jeopardy! contestant says that mastering the buzzer is part of the winning strategy. Many nonwinners complain that their downfall wasn't the questions as much as the buzzer. After Trebek finishes reading the question, lights come on indicating that it's okay to buzz in. Buzz too soon and you can be locked out. Buzz too late and an opponent gets the chance to answer.
Look for Clues
Most Jeopardy! questions contain several clues that can point you to the answer. You don't need to know the answer to both clues to answer correctly. For example, a question from an actual archived show reads, "In the 1860s, it became the last of 4 capitals to be named for a U.S. president." Your clues are U.S. president, capitals and 1860s. You don't need to know what capital was the last to be named after a president. You just think "1860s president," and it's a good bet the answer is Lincoln.
Practice
Ask friends and family to ask you questions. Take note of categories you miss consistently and therefore need to work on. Practice actual Jeopardy! games by playing along on TV, online and anywhere you can.