Open Whisper Systems created Signal (Private Messenger) to make encrypted communication simple. It is available on iOS and Android. And they are working on a Desktop/Web version.
The Electronic Frontier Foundation (EFF [@EFF]) recommends it and has offered some guides on their site for the iOS and Android versions. Here is some information about how to get it and use it.
iOS Version
Get it on the App Store: https://itunes.apple.com/us/app/signal-private-messenger/id874139669?mt=8
Read the how-to guide from EFF: https://ssd.eff.org/en/module/how-use-signal-ios
Android Version
Get it on the Google Play Store: https://play.google.com/store/apps/details?id=org.thoughtcrime.securesms
Read the how-to guide from EFF: https://ssd.eff.org/en/module/how-use-signal-android
Desktop Version
And they are working on a Desktop/Web version: https://whispersystems.org/blog/signal-desktop/?ref=2677989.
More Information
Do you want to learn more about how to protect yourself from ubiquitous online surveillance? The EFF has put together this list of tips, tools and how-tos for safer online communications at https://ssd.eff.org/.