Matrix is a federated communications system, typically for multi-user chat, with end-to-end content security features. You can consider it to be like a modernized version of IRC chat where the crypto and access controls have been built in by default. At present Matrix is really only a creature of the clearnet and so there isn't any way to protect the metadata. Despite the talk of security the lack of metadata defenses make this really only suitable for public communications, similar to microblogging or public IRC channels.
Another consideration is that since matrix operates on the usual HTTPS port number (443) this may make it difficult for ISPs or governments to censor this type of communications via port blocking without significant blowback.
Log into your system with:
ssh myusername@mydomain -p 2222
Using cursor keys and Enter key select Administrator controls and type in your password.
Select Add/Remove Apps then matrix. You will then be asked for a domain name and if you are using FreeDNS also the code for the domain which can be found under Dynamic DNS on the FreeDNS site (the random string from "/quick cron example/" which appears after update.php? and before >>). For more details on obtaining a domain and making it accessible via dynamic DNS see the FAQ. Typically the domain name you use will be a subdomain, such as matrix.mydomainname.net. It will need to be a domain which you have bought somewhere and own and not one of the FreeDNS subdomains, otherwise you won't be able to get a SSL/TLS certificate for it.
Go to the Administrator control panel and select Passwords then matrix. This will give you the password to initially log in to the system and you can change it later from a client app if needed.
Install the Riot app from F-droid on a mobile device. You can then log in with your username and password, making sure to select a custom server and then entering your Matrix domain name for both the main server and identity server.
Other client apps are available but are currently mostly only at the alpha stage. You can also install the Riot freedombone app if you need a user interface for desktops or laptops.
It's recommended that you add an SRV record for Matrix to your DNS setup. How you do this will depend upon your dynamic DNS provider and their web interface. On FreeDNS on the subdomains settings in addition to the subdomain which you are using for the matrix server create an extra entry as follows:
Type: SRV Subdomain: _matrix._tcp Domain: [youdomain] Destination: 10 0 8448 [yourmatrixsubdomain]
You may also want to make another entry with the same settings but replacing tcp with udp.
If you're using the Riot mobile app to access your Matrix homeserver then you can significantly improve battery performance by going to the settings and changing Sync request timeout to 30 seconds and Delay between two sync requests to 600 seconds. Also turning off msgs in group chats will help, since it will avoid getting a notification whenever a group chat event happens, which then wakes up the screen.