The story of Fallout is a mass amount of stories from games, books, and other pieces of lore that seen within the world of Fallout. A few of the more well known stories in the Fallout Fandom will be spoken of.
Fallout One has the player at the start searching for a Water Chip to save their vault from dehydration. Along the way you come to settlements like Shady Sands, The Hub, Boneyard, and Necropolis ; these places are major locations. You'll also come across enemies and future factions such as the Super Mutants of the Unity and the Brotherhood if you find their base. In the early game, Unity isn't mentioned until you reach Necropolis.
Once you have obtained the Water Chip and return to Vault 13, you are told by the Overseer to wipe out the Mutant threat somehow once the Waterchip is returned. This resulting in you exploring the rest of Southern California and stopping the Mutant threat at both Mariposa and a place south of the Boneyard known as the Catherdal where a vault known as the LA Vault is. Once you defeat the Master whether by causing him to lose hope and kill himself or fight and run out as the Vault self-destructs, you are brought back to Vault 13's entrance where the Overseer banishes you from the Vault. You can kill the Overseer if you have bad karma or are just quick enough to shoot him, giving him a unique death animation.
In the aftermath of Fallout 1, Shady Sands would band together with the other major settlements to make a new nation known as the New California Republic, becoming more important for Fallout 2 and New Vegas as a major faction and the only real 'nation' in the world of Fallout.