Noting that I am not an expert in this matter, based on my own experience I can offer the following advice. In order to enter Mexico with a residency visa with permission to work, you must have a job offer from a Mexican employer in hand and apply for the visa from outside of Mexico. It is possible to come to Mexico first on a tourist visa and look for work while you are here, but once you have a job offer you will have to leave Mexico and start the process from your home country. This can cause delays which might make a potential employer think twice about hiring you, so it really is best to have the job offer before making the move.
Although it is relatively easy for Canadians and Americans with certain skills to work in Mexico, it is important to understand that non-Mexicans cannot be hired for a position if there are qualified Mexicans who can do the job. Non-Mexicans who want to work in Mexico should have a skill that is not available locally or specialized professional credentials. Under the terms of NAFTA, certain professional categories are automatically allowable.
Native English skills are a valuable asset that might make it easier for people to obtain job offers from Mexican companies if they also have in-demand skills or credentials. But be aware - lots of young people in particular think of going to Mexico and teaching English and are surprised to discover that it is not enough just to be able to speak English. Assuming that you want to work legally rather than under the table, you will have to have some formal teaching credentials in order to be employed by language schools or for teaching positions in international schools.
(Travel to Teach Mexico, logo, pictured.)
If you have an internet-based business and you do business internationally, you can work in Mexico and draw your paycheque from abroad without requiring any special permit. It is also possible to obtain a work permit as a self-employed freelancer if you have a skill that you use to generate income in Mexico.
Whatever your employment situation, it is a good idea to be aware of the general requirements and procedures from official online sources, but it is a better idea to actually speak to the people at the office where you will be making your application. Although there is a common legal framework regulating all of this, sometimes you will find that things are interpreted differently in different locations or circumstances. This is related in part to the fact that there was a major overhaul of immigration laws in 2014 and there is still some fine-tuning going on with respect to how these new laws are applied.