Elysium can be played via a web client on this website, which you can access by clicking here.
However for a better experience you may wish to download and install a MUD client, which will allow you to customise the visual experience, as well as set up shortcuts and highlights which can make playing a MUD easier.
Although there are multiple different MUD clients available, one of the more common (and free!) options that players use is mushclient.
Once you've downloaded and installed a client of your choice, you will need to enter a 'world address' to connect to Elysium using your new client. The 'Address' of Elysium is elysium-rpg.com and the 'Port Number' is 7777. If you've chosen to download mushclient, your configuration screen should look like the below image to connect to Elysium.