Drizzt Do'Urden was born in Menzoberranzan deep below the deepest caves in a land called the Underdark. He was taught by his sister Vierna until he became sixteen. Then because of Zaknafein (his real father) he was trained to be a warrior, instead of a wizard.
Drizzt, after training with Zak, went to the Academy, Melee-Magthere, where he was to learn about the drow and to train more in combat situations. During the Grand Melee, Drizzt teamed up with a classmate who "killed" him right after Drizzt saved his life. It was then that he learned just how evil the drow are. The next years that he was in the Academy, he teamed up with none, and won. Drizzt, after Zak willingly sacrificed his life for him, ran into the Underdark to live there.
In the Underdark, Drizzt lost all track off time, and if it wasn't for his friends Guenhwyvar, Belwar Dissengulp, and Clacker, he would have never lasted against his family chasing him to regain Lloth's favor.
To try and escape from the drow, Drizzt went to the surface. There he was hated by those who he tried to save. He eventually found his way to a blind old ranger named Montolio DeBrouchee. After becoming best friends, Montolio teaches Drizzt all about the surface world and all those in it. He teaches Drizzt about Mielikki, the goddess of the rangers' heart. To Drizzt she was not a goddess, but a way of life. After Montolio died, he went around the realms, being shunned away at every city until he ended up in Icewind Dale. He wasn't allowed in the only cities in the area, Ten-Towns, but he was allowed on the opposite side of the only mountain, Kelvin's Cairn. Here he meets his life long friends and his life truly begins anew.
He travels with his friends to distant places, from the icy glaciers above Icewind Dale all the way to the hot Deserts of Calimport, and over as far as Mithril Hall and Silvermoon. Along the way, he meets some more friends as well as some enemies. Using the skills that he learns throughout his travels, he manages to always land on top of the situation. As he travels with his friends he learns that none of the places are really his home; that his home is with his friends.
Drizzt is a ranger, and follows after the heart of Mielikki. He is one of the finest fighters in all of the realms, but has the biggest heart of them all. He is kind to all and tries not to judge anyone. He is always there for his friends and never lets them down if he can help it.
I could go on and on about Drizzt Do'Urden, but the only way to learn about him truly is to read for yourself. Enjoy!