The goal of this game is to connect 4 or more puyos together to make them pop, and send some junk over to your opponent, or reduce junk that is waiting to drop on you. You want to try and make combos to exponetially increase the amount of junk you send over. If you see junk waiting at the top of your screen, the next time you drop a puyo without breaking anything, that junk will fall on you. However, if you continue to break, you will delay the dropping of the junk. Everytime you have junk ready to drop on you, and you break something, you reduce the amount of junk dropping, and you also do what is called "displace". When you do this, your Fever meter will increase by one point. Once you Fever meter is full, you go into Fever mode where you are give pre-built combo chains. All you have to do is trigger the combo, and you for huge chains. If you are having trouble figuring out how to combo some of the chains, just watch what the AI does.
So basically, you need to destory your opponent. This game is quite good since it actually involves strategy