Why does Siddhartha search for enlightenment and how did he achieve it?
What is interesting to consider, too, is what Siddhartha does first in his search for enlightenment and how he, at first, fails to achieve it. He starts off pretty much by going from the one extreme that characterized his life (excessive wealth, unquestioned privilege, etc.) to another extreme (complete rejection of materialism: no money, no cooked food, no bathing, etc.). He realizes that the one extreme is no better than the other; to the horror of the group of mystics and aescetics who had come to look up to him in his rejection of the material world, he accepts cooked food from a woman and bathes in the river.
Hermann Hesse's novel Siddhartha (see the link to the study guide) is one of many treatment of Siddhartha's quest for enlightenment. Hesse adds elements, I think, that are not common to other versions. Most versions agree, of course, that enlightment is attained not simply by rejecting the world but rather by freeing the mind of distractions, by not giving in to tempations, and by seeing past the illusions of the world around us.
The probing and questioning nature of existence is what drives Siddhartha to strive for Enlightenment. Born a wealthy prince and living the life of royalty, there was a part of him that wondered about issues of life, death, and the nature of suffering. Upon leaving his palace one day and seeing an old man who is dying, the prince realizes that his regal life will preclude him from understanding the true nature of existence. This is what motivates him to leave the palace in search for enlightenment and understanding the essence of consciousness. Through isolation and meditation, Siddhartha learns to shed through the layers of illusion in embracing the true form of existence and enlightenment.