The battle screen is shown in the figure below. The bottom part is your block teritory whereas the top part is your opponent's. Touch a block on your teritory, move it to another place wherever you want, and just release it. That is all the basic operation you should master in the game!
Next lets learn how to delete blocks. The rule is quite simple. Four or more blocks of the same color which are connected will be deleted. Note that the connection needs not to be in a line, but it must in horizontal or vertical direction, not in diagonal. See the sample of connections in the figure below.
Once blocks are deleted, the blocks on the deleted blocks will fall down. After the blocks fell, the connection will be checked again. If there are blocks in connection again, the blocks are deleted. If there are no more connection, new blocks will be supplied from the top and the connection check will run again. Like this manner, we can get a chain of delete-fall-delete block, which is simply called "chain".
Once you deleted some blocks, depending on the weight of the deleted blocks, some fire balls are send to your opponent. The fire balls are stocked in the fire ball region (located on the top of block) until your chain finish. As your chain finished, the launch bar (located on the top of block) starts to decrease. When the launch bar becomes zero, the fire balls are launched to your opponent blocks and burn out the blocks.
The burnt block, called kurosuke, can't be moved. If you delete some blocks and there are kurosukes at their neighbor, the kurosukes will be deleted together. If your region is full with kurosuke and you have no move to delete block anymore, then you lose.
Usually when you are sending fire balls to your opponent, your opponent is also deleting blocks and sending fire balls back to you. In that case, the sending and receiving fire ball count will be cancel each other. So don't be panic when you receive many fire balls. You still have a chance to cancel it by creating more chain. But the time is short, so you have to hurry!