As would be suggested by the name, the central Pagoda is a key point to making your chain of pieces. Due to this, the three entrance points are also very important. Much of the game revolves around controlling them.
In general you should not kill your opponent as the first person to get a budda has a definite advantage. What makes this game intriguing is the constant playing of the odds. Force your opponent to continually capture you so you get a budda, in all likelyhood, before they do.
You can use your goats on the outermost ring to push a piece in one of the three pagoda entrance points up to the pagoda. This also installs your goat in the entrance point. This is a way to have a threat of suddenly adding a connecting piece where there was not one before.