The only airport in this region with scheduled commercial service is at Silver City, with extremely limited commuter service to Albuquerque. The nearest significant airports are in Albuquerque and El Paso, Texas. Interstate highway 25 passes through the region north-south from Albuquerque to its junction with I-10 at Las Cruces. Bus lines follow this route, with some digressions into small towns in the region, but service is generally fairly limited. Amtrak's Los Angeles - New Orleans Sunset Limited (http://www.amtrak.com/ser...) route passes through the region, stopping in Deming and Lordsburg.
Although the region has a long border with Mexico, legal! entry from Mexico is only possible at a few locations. The entries in the region itself are crossings at Santa Teresa (http://www.cbp.gov/xp/cgo...) in Doña Ana county and at Columbus (http://www.cbp.gov/xp/cgo...) in Luna county. Much more traffic enters from Juarez near El Paso (http://www.cbp.gov/xp/cgo...) and heads north from there. There are checkpoints along the major arteries from El Paso/Las Cruces where the Border Patrol may check for illegal immigrants, smuggled goods, etc. They generally don't hassle travelers on routine business; don't break any laws and you won't have any problems there.