You are not allowed to work on a Tourist Visa. As a Temporary Resident, you can apply for a work visa, they will determine whether you will receive permission – only then can you apply for work. Be patient, this can take 30+ days. As a Permanent Resident, you can work here – you must report to the Consular office to report your employment information. You’ll need a document from your employer.
They say that you cannot have a job that would take away from a Mexican but I haven’t found this to be entirely true. Keep in mind that the average daily wage in Mexico is less than $8 US dollars PER DAY. So be sure to do your research on the pay rate before you get to far into the process.
Check in with an immigration attorney if you are considering working here and earning pesos.