Retrieve the GECK for Arroyo

This is the main starting quest given to the Chosen One at the beginning of Fallout 2.

There are two GECKS in the game, One at Vault 13 and One at the Final Base.

In order to retrieve the GECK from Vault 13, one must make his way to NCR, talk to the Sheriff standing on the corner, tell him you're looking for "honest work." He will then refer you to Westin (the entrance to his ranch is appropriately enough at the west end of town). Take the quest to investigate raids on his brahmin and then track the perpetrators back to Vault 13. At the Vault you will have to either negotiate with or dispose of the inhabitants.