In Hindu Mythology, the Trinity usually refers to the Trimurti: the three persons of God as Creator, Preserver, and Destroyer.
The Creator God, Brahma, is usually portrayed mythologically as a fair man with four arms and a white beard. His wife is Saraswati, the Goddess of Knowledge. Both are associated with knowledge, and Saraswati (who is more popular in devotion than Brahma) is associated with learning, art, and music. She sits atop a swan, and plays the veena or vina (an ancient Indian stringed instrument; an ancestor of the sitar. See Ravi Shankar).
The Preserver God, Vishnu, is often portrayed as blue with six arms. He is the focus of a large cult in Hinduism, and is believed to have come down to Earth in human form in various avatars. The ten traditional avatars are including: Matsya (the fish), Kurma (the turtle), Varaha (the boar), Nrsimha (the man-lion), Vamana (the dwarf), Purusuram (the man with an axe), Rama, Krishna, Buddha, and Kalki. Rama is the ideal man (as son, brother, husband, father, king, etc.) and is the focus of the Ramayana epic. Krishna is the focus of many legends as a child in the Puranas (some scholar believe that the devotion of missionaries to the Infant Jesus influenced this), and he is a central character in the Bhagavad Gita, part of the Mahabharata. Buddha is famous as the founder of a new religion (as such he is not particularly important to Hindus). Kalki is the avatar that has been predicted, but has not yet come. This could potentially be the focus of some apocalyptic cult, but I don't know of any.

Vishnu's wife is Lakshmi, the Goddess of Fortune and Prosperity, who sits atop a lotus. An Indian company specializing in food products is named after her, spelled Laxmi.

The Destroyer God, Shiva (or Siva), is also the focus of a great cult in Hinduism. He is often the most difficult God to understand; he is portrayed as the extreme ascetic, covered in ash with matted locks, often in meditation. He is associated with snakes, and his head is the source of the Ganges river. One of his most popular forms is the Nataraja, in which is portrayed dancing with many hands in a Cosmic Dance of Destruction, often standing over a vanquished demon.

Some devout believe that Shiva also came down in avatar form; the most famous example would be the saint Shankaracharya, who wrote many Hindu scriptures and was largely responsible "winning India back for Hinduism from the Buddhists."