Most every population center in Mexico has high-speed internet service. Availability and quality of service varies but you will find DSL, cable, and cellular service throughout the country.
The major cellular providers in Mexico are Telcel, Movistar and now AT&T. Roaming services are provided to compatible foreign phones but roaming costs are entirely dependent on and set by your home provider. Often it is advantageous to buy a pay-as-you-go SIM chip in Mexico. This gives you a Mexican phone number, local and long-distance calling, and data services. SIM time can be purchased at many local stores or online.
Land lines in Mexico are mostly provided by Telmex or Telnor. Often bundled with other services such as internet and Claro Video (Mexican equivalent to Netflix) for one low price. Plans often include unlimited long distance calling to any North American number for free, but local calls to land lines or cell phones have limits.
Some expats bring their satellite equipment with them and continue to use it in Mexico. Even Canadian satellite services from Shaw Communications can be tuned in, although this is provided through older Shaw satellites that are due to be decommissioned soon.