I am a current resident of the USA with a visa that will expire in 4 years. I currently live in New Mexico but hope to travel to California next month. Can I travel by plane? If so, do I need a passport and how or where do I get it?

Sincerely
Rocio

Traveling by plane is no problem at all. You will need to have government-issued ID with you when you travel, and also be sure that the name on your ticket matches the name on your ID. The ID could be a passport, or drivers license issued by a US state - see the TSA website for a complete list of acceptable IDs: TSA: ID Requirements for Airport Checkpoints