When searching for a person in Mexico, going to the country yourself yields the best results. No notable websites exist that allow people to search for individuals only in Mexico. However, Mexicans widely use Facebook, so you can try performing a search there.
If it is not possible to travel to Mexico to perform a search, the next step would be to find out if the missing person has any relatives or close friends that live in the United States, and look for them. Once a relative or friend is tracked down, try to find out as much information about the missing person as possible if the current location is unknown. It might be helpful to ask about the missing person's last known location, where he might have gone, if he has any relatives or friends in Mexico, if he ever spoke about going there and anything else that might be helpful. If the missing person has a unique last name, a good idea is to try searching for people with the same name; maybe they are relatives with the missing person.
Another tip is to obtain a SIM card by Telemex or find somebody who has one, and use the company's website to search for the missing person. There is a large chance that the missing person uses the same phone company. Hiring a private investigator is another way to find a missing person, but it may cost a lot.