It's not hard to find work teaching English in Mexico, although most of the jobs will be found once you are there, rather than online. There is a strong demand for English teachers. Mexico City is the main TEFL destination in Mexico, but there are teachers teaching English in Guadalajara, Acapulco, Monterrey and many more cities and towns in the country.
Pay for teaching English in Mexico is low - however, if you have recognized teaching qualifications and experience in your own country you can work in an international school, where the pay is much higher. For TEFL teachers, privates pay around 100-250 pesos an hour in Mexico City and the larger cities. In smaller provincial cities the pay is lower, around 100-150 pesos an hour.
Language schools, where most teachers will be working, pay around 40-75 pesos an hour in Mexico City. Less in the provinces. Salaries are around 4,000-10,000 pesos a month. Language schools in the provinces pay around 3,000-7,000 pesos a month. Not a huge amount. If you require your own apartment, expect that nearly all of your salary will be needed.
It's best to look for work after you arrive, but there are jobs advertised online. For those looking for work in public schools or universities, check the institutions own websites. Dave's ESL Cafe and TEFL.com also have some job ads for ESL jobs in Mexico.
Demand is strong for native speakers with a degree and TEFL certificate, however, none of these are absolutely necessary. The more of the above qualifications that you possess, the better the school you will end up in - as a general rule.
Tourist visas - for most nationalities - are 180 days. These are non-extendable. It is - at present - possible to border hop, coming back on a new visa. It's illegal to teach English on a tourist visa, although many people do. You risk deportation, if caught. Schools can sponsor you for a work visa.
Language schools in Mexico have the usual problems of split shifts that exist all across the TEFL world. This may be exacerbated - depending on whereabouts you live - by Mexico City being one of the biggest cities in the world - with a metropolitan area of over 21 million people. A good source of information for those who wish to teach English in Mexico, and for teaching English in Latin America generally, is LA Job List. Here is a list of schools in Mexico on that site.
Speaking Spanish will help you find work and enjoy living in Mexico, but courses can be expensive. You might want to consider studying in Guatemala – one of the cheapest places in the world to study Spanish – and then going to Mexico to find work. See my article on Teaching English in Guatemala.