A good way to earn neopoints is to scout out the games that give you the most neopoints. You can also try to do the Wheel of Excitement, the Wheel of Knowledge and the Wheel of Mediocrity.
You also have a chance of winning big in the stock market under board games in the games room. If your pet is really really hungry and you have less than 3,000 neopoints you can get food at the soup kitchen.
Exploring the Neopian world is also a good way to get knew things and earn neopoints. On Terror Mountain there is a game called snow wars that is like battleship and you can earn trophies and medals.