Shiva reperesent destruction, austerisity and the most maligent force of life.This should be seen in the context of creation and the destruction being a continuous part of the life cycle.
Shiva was not a Vedic God but hisspritual ancestor , Rudra is mentioned in the RIG VEDA.In the form of Supreme Being(Mahadev) he is shown as the phallic symbol(LINGA)in conjuction with the female organ(yoni)which are often the point of worship in the Shaivite temple.

He may also hold a small drum(damaru) and wear a tigerskin and jewellery in the form of snake.
Shiva is responsible for the devastation of the universe. His symbol are not only characteristic of his purpose, but are also almost too numerous to name. There are some that are shown with him in almost every picture.

Trident -- the symbol of Shiva's strength

Drum -- symbolic of rhythm and sound

Bull -- called Nandi, is Shiva's vehicle; Nandi also symbolize Shiva's command over sex and sexual behavior; and represents strength and happiness

Snakes -- show that Shiva is out of the power of death even though he is surrounded by it (around his neck).

River Ganges -- flowing from his hair, depicts the water from which the earth arises

3 Eyes -- symbolize the sun, the moon and fire, the three sources of light, life and heat

3rdEye -- affirm the eye of knowledge and wisdom

Ashes -- which cover Shiva's body,show that Shiva is God of Destruction