For example, if you want to join Freenode #lisp channel via Matrix, you can do so by joining #freenode_#lisp:matrix.org. Here is a direct Element web client URL to it, in case you want to try it now: https://app.element.io/#/room/#freenode_#lisp:matrix.org .
Element (previous known as Riot) web client is a great way to get started with Matrix without having to install anything. You have to create an account of course but after that it is pretty straightforward. The fact that all of Freenode (and now Gitter) is available on it makes it like one big IRC bouncer. Moreover, this is all distributed and decentralized!
Here is another safe Matrix room to try out and experiment with: https://app.element.io/#/room/#spxy:matrix.org . Most of us here are from Hacker News. We talk about computer science and mathematics here. Common Lisp and Emacs are being discussed these days. Say "hi" if you join it! :)