A visit to Mexico to stay in your new home is a simple process; just fill out the Tourist Card (FMT) available to tourists from all airlines and at all ports of entry to the country. This permit allows visitors to stay for a maximum of 180 days, provided they do not participate in any remunerative activities while they reside in Mexico. More information about the different kinds of visitor permits issued by the Mexican government can be found here:

Mexican Immigration and Visas
If you decide to move or retire to Mexico, however, the process becomes a little more involved. For those over 50 years of age who wish to retire in Mexico, a Retiree Immigration permit must be obtained. This permit requires that you not participate in any remunerative activities while living in Mexico, and that you have or are receiving sufficient funds (from a retirement plan or pension in your home country) to live in Mexico. The amount of funds required is subject to change. For those under 50 years of age who choose to work in their new country, an FM3 permit must be obtained. Your local Mexican Consulate can tell you both the process for applying for this visa and the amount of funds you need to be granted the permit. A list of Mexican Consulates can be found here.

Directory of Mexican Consulates Abroad