Most travelers will be given their tourist visas on the plane (I’m sure there are countries in which you have to apply first, though I don’t know which). The tourist visa is an unassuming little piece of paper that the immigration authorities will stamp and then give back to you with the number of days you can stay (no fewer and no more than 180, by law). This visa does not allow you to officially work or do any lucrative activities. Make sure you don’t lose it, as you will need it to leave the country (unless you have another type of visa). There are fines (and possibly airport delays) if you don’t have it. If you DO lose it, you’ll have to go to the Ministerio Público to make a legal declaration.
Work Visas in Mexico
As of 2013, there are new rules for work visas, and I am no longer familiar with them. I do know that you need a letter of invitation to come and work at a school here (if you do not already have a Mexican work visa), and if you came in on a tourist visa, you will have to leave the country and apply for your work visa at a consulate. This website provides a rundown of the new visas and requirements: http://rollybrook.com/living_in_mexico.htm
One tip that I have is to get any important documents– namely your birth certificate and any school diplomas– notarized and apostilled before you come. The apostille can only be given in the country in which the documents were issued, and since FedEx is quite pricey, it’s always a good idea to try and get those documents in order before you arrive!
*Disclaimer: You should check the visa requirements at your local Immigration office or online before you start the process.