Founded in 2142 by one of the groups emerging from Vault 15, it was jump-started using the GECK, which allowed the dwellers to establish a self-sufficient community and erect adobe buildings. In the 2241|2240's, the small settlement grew and expanded, forming one of the most influential cities to emerge in the mid-23rd century, the New California Republic.
By 2161, it was a small, thriving, completely self-sufficient community, as they managed to adapt some of the wasteland soil to support crops, (primarily corn and cabbage), drill a well to provide them with water and even establish a brahmin herd. They kept mostly to themselves and proved large enough to deter most of the problems the Wasteland presented, primarily the Khans raiders and the radscorpion attacks that plagued them. Both of these threats slowly escalated, as radscorpions were becoming more and more numerous and aggressive, while the raiders seemed hell bent on bringing them excitement at any cost. Their agriculture, while managing to sustain them in the arid region, was lacking as well.
These problems were alleviated by the Vault Dweller, who discovered the settlement en route to Vault 15. Initially distrusting, the inhabitants quickly warmed up to the hero as he/she proceeded to eliminate the radscorpion threat, and later rescued Tandi, Aradesh's daughter, from captivity, and possibly death at the hands of the raiders.
The town is typically the first settlement after Vault 13's caves that most players visit, due to its location along the path between Vault 13 and Vault 15, the vault the player is advised to travel to at the start of Fallout.
If you encounter a traveling merchant outside of Vault 13, he will explain that he is traveling to Shady Sands, and asks if the player would like to be escorted there.