Protocol website: https://xmpp.org/
XMPP is a messaging protocol, as such, there is a great deal of flexibility in how it is used. Servers may be public or self-hosted, and clients are available for all platforms.
For a list of recommended software, see: XMPP- Software
I recommend Cheogram for Android. This app allows you to create a free account on any one of several servers, or multiple accounts for privacy. It can be downloaded from F-Droid: for Android installation instructions, see this page: Installing Apps with F-Droid
For Linux based OS, such as Ubuntu or Debian, Dino works well.
There is also the web client ConverseJS
After choosing a program, create an account. Cheogram and Dino allow you to register an account on one of the default servers configured in the program. You will have to create a password and username: record these for later use. You can also choose another server, such as a self hosted one.
After launching a new app (such as desktop client) you can sign in to this account using the same credentials.
One-on-One chats can be encrypted using multiple methods. OMEMO encryption is likely the most secure, but requires some care in setup, as keys must be confirmed on any devices added to the same account. If using only one device there is no problem, but keys must be confirmed on your contact's devices for maximum security. OMEMO uses Double Ratchet encryption, making a Man-in-the-middle_attack difficult or impossible.
The webmaster can be reached at XMPP user: baptistlibrary at yax.im