By Rail
The Southwest Chief (http://www.amtrak.com/ser...), the main Amtrak line through the southwestern United States, makes a daily run between Chicago and Los Angeles through New Mexico. Westbound, the line enters the state at Raton, and basically follows the route of I-25 to Albuquerque, making stops at Las Vegas and Lamy where you can catch a shuttle bus to Santa Fe. After Albuquerque the train follows the route of I-40 to Gallup and on west.
The Sunset Limited (http://www.amtrak.com/ser...) makes its way from New Orleans to Los Angeles, with stops at El Paso, TX, Deming, and Lordsburg. This train runs three times a week.
The Cumbres and Toltec Scenic Railroad of Chama New Mexico and Antonito, Colorado operates tourist trains with vintage equipment passing attractive scenery, but this line doesn't connect to any commercial railroads and isn't intended to open the state to the traveler from afar. There are presently no other rail services from other states or Mexico to points in New Mexico.
By car
Interstate highways 10 and 40 cross the state east/west, the former entering between El Paso and Las Cruces and paralleling the southern border, and the latter following the route of historic Route 66 through the middle of the state. Interstate 25 enters the state in its northeast corner near Raton, passes through the eastern plains, crosses the Sangre de Cristo Mountains at Glorieta Pass near Santa Fe, then follows the Rio Grande south through Albuquerque to its terminus at I-10 in Las Cruces.
Although New Mexico has a fairly long border with Mexico, there are few ports of entry. Most traffic inbound from Mexico enters the United States at El Paso and then continues to Las Cruces and beyond. In addition to the usual customs, etc., at the national border, there are checkpoints along the major highways out of Las Cruces at which vehicles may be searched for illegal immigrants. If you're considering bringing an illegal in, don't; penalties are serious and enforcement is stepping up, if still uneven. The small town of Columbus has a border crossing with Mexico that is open 24 hours a day. Santa Teresa NM, adjacent to El Paso and south of Las Cruces also has a port of entry. Although this border crossing is only open from 6AM-10PM, it forms a handy bypass of Ciudad Juarez and El Paso and is an important route for international commerce and travel.
In practice, traffic inbound from neighboring states is generally not subjected to inspection for controlled items, apart from the usual weigh stations, etc., for commercial trucks. However, commercial traffic heading out of New Mexico for Arizona may be inspected on the Arizona side of the state line, owing to concerns about the introduction of agricultural pests.
By plane
The state's only major airport is in Albuquerque, in nearly the exact center of the state. Santa Fe has limited connector service. Several of the state's minor cities such as Carlsbad, Farmington, Roswell, Hobbs, and intermittently Gallup and Taos have commuter air service.
For travel to the southern part of the state, particularly the southwestern region, consider flying into El Paso in extreme west Texas. For example, Las Cruces, the state's second largest city, is only 45 miles from El Paso compared to 226 miles from Albuquerque.