Buddhism is an outgrowth of Hinduism. Hinduism and Buddhism alike teach man is trapped in an endless cycle of reincarnation. The goal of the Buddhist is to escape this cycle and go back into Nirvana, which is defined as the nothingness from where he came. This is not the same thing as the Christian concept of heaven, where you continue to exist. This is a total extinction of life. No individual has a soul. Basic concepts include pantheism and Self-salvation.

Gautama Buddha was a Hindu priest in India around 500 BC. About 477 BC, after the death of Gautama, his disciples put together the Sutra's (Sayings of Buddha) and the Vinaya (rules and regulation of the Buddhist order). Together these form the Dharma (teachings of Buddha).

In 245 BC the third Buddhist council was held. This formed a definitive cannon called the Pali texts.

Types of Buddhism

Theravada: This is the oldest school of Buddhism. They follow the Sutra and Vinaya very strictly. They consider Buddha a great ethical teacher. Only Buddhist monks are allowed to study the Sutra and Vinaya. Buddhists are encouraged to become Arhats (Buddhist saint who have achieved their own deliverance from the cycle of reincarnation). Nirvana is not limited to monks.

Mahayana: This school formed about 400 AD. They consider Buddha to be a god. Everyone is allowed to study the Pali texts. Nirvana is reserved only to those who follow the discipline of the Pali texts rigidly. Buddhists are encouraged to become Bodhisattvas (people who are destined for Buddha-hood, or Godhood, but delay this for the purpose of teaching others) 

Zen: This school of Buddhism formed in Japan. It teaches that one reached enlightenment through certain ways of meditation and thought. This can not be defined or put into words but must be experienced.

Tibetan: This school formed about 700 AD. This is basically Buddhism mixed with Shamanism, magic, and nature worship. While in the other forms of Buddhism the monks are celibate, Tibetan Buddhist practice Tantra. Tantra teaches a method of a obtaining enlightenment, or Godhood, through sex. The dark side of Tantra is very perverted. They have also borrowed the concept of the Mantras (repeated words or phrases) and Mudras (physical positions) from Hinduism.
The Dali Lama is the Leader of this form of Buddhism. It is also called Lamaism.