I don't know about the rest of the West, but in Arizona, generally you need a B.A. in Anthropology to get hired as a field tech. It is preferred that you have attended a field school (or have a basic understanding of archaeological field methods). A crew chief/field supervisor usually has a B.A. degree, plenty of field hours under their belt, and knowledge of the region's culture history and material culture. To be permitted by the Arizona State Museum to direct field projects, you'll need an M.A.

In the west the majority of the land is government owned, most SOI. So to become a crew chief or above you need to meet the SOI standards, usally an MA http://www.cr.nps.gov/local-law/arch_stnds_9.htm. Most job adverts will say need to be permited etc. that is meeting the SOI standards and sometimes more. The BLM usally requires their own permitting standards and that differs from state to state. For exmaple in NM there are 5 areas (navajo, nw, ne, se, sw) you can get a permit in and they all require 40 days of survey and 20 days of excavation in each area. Chris from ramdom acts of science moved from east to west. He worked from state to state across the country so that he could qualifiy for the "local/regional" exp. that is sometimes required to get a job. If you contact him I am sure he can tell you more. He also works in NV so he can tell you about that.

In the past, it was much more difficult to break into the west without prior experience in that state/region.  It has, however, become much easier the past couple years due to the notable paucity of field techs and crew chiefs.  You'll still need a field school, BA, and a few months experience, and a little luck.  As far as crew chief's go, the State of New Mexico requires the registered crew chiefs to have an MA or enough experience to satisfy a certain level of competency.  DougRM is right about Federal lands, you will generally need to meet the DOI requirements to be a crew chief, and some Federal agencies, such as the BLM in New Mexico, will impose additional restrictions for the crew chief/field director role (correction for DougRM - it's actually 80 days of combined fieldwork in that specific area, with at least 60 survey days and the remaining 20 days either survey or excavation).