To become the "Champion", you must answer all 15 questions correctly in a game taking up to the 1,000,000 mark.
To start a cooperative game from the main menu, click "Play" > "Local Multiplayer" > "Cooperative". Then select your controllers, select your character and begin.
The first five questions are the easy ones and even if you are unsure it is usually pretty obvious what the answer is by the options you are given. From here the questions become increasingly more difficult. Here are some tips for getting through all of the questions:
1. Select question categories that you know.
2. Use your lifelines wisely. Try to save them for the later, more difficult questions. That said, if you really don't know the answer using a lifeline is better than starting over.
3. Try to answer the earlier questions quickly in order to "bank" the timer for the final 1,000,000 question.
4. Do not skip the speech in between questions. Your timer won't start until all of the answers are displayed on the screen but if you skip the speech, it will jump straight to all four answers meaning you have to read them quickly wasting valuable time.
5. Have a computer to hand for the more difficult questions. If you are quick, you will be able to search the internet for the correct answer before the timer expires.
If all else fails, you can always restart a game and try again with different questions.