WhatsApp is the preferred method for text communication in Mexico. It is very simple to use and links to your mobile number. WhatsApp uses the internet connection so you can avoid any international SMS fees.
Check with your mobile service provider for coverage in Mexico City. T-Mobile, for example, offers free data and calling in Mexico. If not free, daily rates will be low cost and worth it to have access. Not sure? When you land, turn off Airplane Mode and your carrier will alert you to cellular and data costs, if any.>
Although Mexico City has a robust public wi-fi service, you may not always have access to your phone. Try the analog way by using a phrase guide. Here are few options:
Lonely Planet guide to Mexican Spanish
Rick Steves Spanish Phrase Book and Dictionary
It is also helpful to download a translation app, like GoogleTranslate. This app is free and allows for several means of translation, including a conversation feature to help with audio translation during conversations and a camera feature to translate text with your camera in case you need to read a sign, menu, etc.