It’s not that hard, but skip the airport and head into town.
It’s surprisingly simple to get connected once you arrive in Mexico.
To begin with, if you’re coming from the U.S., it’s worth checking your phone plan to see if it offers inexpensive coverage in Mexico. If it does, you’ll be sorted from the moment you touch down. Because there’s no place to easily acquire a SIM card at the airport itself, you may want to leave your data on long enough to call an Uber to pick you up (your pick-up options will refer to specific doors of the terminal by number), since it’s less expensive than the prepaid official taxis, though that’s also a perfectly fine option.
Once you’re in town, the best place to get yourself hooked up is the stretch of the Eje Central – one of the city’s most important avenues – just south of the Torre Latinoamericana and the Palacio Bellas Artes. On the east side of the avenue (the same side as the Torre), you’ll pass several slightly sketchy looking, semi-open malls called Pasajes or Plazas devoted entirely to phones, headphones, and assorted electronics. Pick one with a big sign for Telcel, the largest provider, and ask for a Telcel SIM for your phone (there are other phone companies, but Telcel is the biggest). The guy at the desk will take care of setting it up for you, a pretty simple process, and you’ll be golden. If you have a broken cell phone screen, it’s probably worth your while to price a replacement here, which will almost certainly cost less than back home.
A bare bones SIM card will cost 50 pesos (about $2.50 USD). For 80 pesos, you can get a small amount of data to start with and get a sense of how quickly you run through it. Refilling when you’ve run out couldn’t be easier. Pop into any Oxxo or 7-11 (there’s one on every corner, almost literally) and tell the cashier that you need a recarga or recharge, for Telcel. They’ll ask for you to pay first—just say how many pesos you’d like to add; start with 50 (cincuenta) and see how that does you–then ask for your phone number (twice), and finally give you a receipt. You should receive a text from Telcel within seconds thanking you for recharging.
Wifi is also surprisingly widespread—even old-school cantinas have it, often as not—so check wherever you go to save datos (data) by asking for wifi (pronounced wee-fee), the network (red) and the password (clave or contraseña).