How would I go about going to Mexico from New Mexico?

Orbitz.com shows round trip tickets from Albuquerque at $1100. That's still a lot. There are buses, but it's sometimes hard to get information on them. Go to Frommers.com and see if there's any advice on the Mexico board.

I found three bus lines that I personally know about in the link below, being number 1, 5, and 18.

Once you get to El Paso, just walk over to Mexico, or transfer/keep riding to San Ysidro/Tijuana.

You can also take Greyhound or another coach bus to San Ysidro, and walk over to Tijuana, MX.

http://www.eplalimo.com/

El Paso-Los Angeles Limousine Express

In Downtown Los Angeles, you will probably have to board a bus operated by a different agency (such as Greyhound/Crucero, Tufesa, or Transportes InterCalifornias).

drive across the border acting like a jesus freak, it somehow works, and is hilarious.

Fly to San Diego. International flights are expensive.

New Mexico is a big state. You need to say where in New Mexico.