Theism simply signifies a belief in a deity.  It is usually used in a very non-specific manner, for instance as opposed to atheism (God does not exist) or agnosticism (the truth about the existence of God cannot be known).  However, theism can be broken down into several distinct types as follows:

Deism believes there is one God or source of reality, but this deity is detached and only semi-personal.  He is not intimately involved in the affairs of his creation.

 Monotheism teaches that there is only one true God, who is personal and intimately involved in his creation.

Polytheism practices belief in and worship of a plurality of personal deities.  Many pagan and tribal religions (both ancient and modern) practice this type of theism.

Henotheism is also a belief in multiple deities, but practices supreme allegiance to only one. 

Pantheism is a belief in a non-personal source of reality, which is in some sense identified with the entire Cosmos. Therefore Nature is God.

Pan-entheism is similar to pantheism, except that God is in some sense bigger than just the Cosmos, while including it within himself.

Absolute Monism is similar to pantheism, except that the cosmos is illusory.  In this type of theirm, God is the Great Unity which manifests itself in the less-than-real world.       

Dualism teaches that there are two opposite and equal deities in perpetual conflict.  The clash of good versus evil deities drives the Cosmos forward.

M. Bogart