Secure instant messaging: a brief guide

So, you’re angry about the NSA logging all your instant messages and phone calls, and want to do something about it? Here’s some info on what you can do. To start off, I assume that your goal is cross-platform secure messaging. That is, solutions which don’t interoperate with other platforms aren’t useful, because not all your friends use the same OS as you. Also not useful is SMS, because not everyone uses their phone for everything.