ViaVersion installation
Installing ViaVersion should be as simple as downloading the plugin or mod's
.jar file and uploading it to your server's plugins folder.
Bukkit/Paper servers
For Bukkit/Paper servers, you can install ViaVersion, which is a plugin.
For server hosts with a plugins tab, you should be able to find ViaVersion
there.
ViaFabric (for Fabric servers)
If your server isn't running PaperMC or another Bukkit-based server software,
but is instead using Fabric, you can install the ViaFabric mod.
ViaFabric and ViaFabricPlus both support clients, allowing players to
connect to servers on any version they want, but ViaFabric also supports
servers. When on a server, ViaFabric works very similarly to how ViaVersion
works, just for Fabric servers.
Important: as far as I'm aware, ViaFabricPlus does not work on servers. Use
regular ViaFabric instead.
Setup
After installing ViaVersion, you shouldn't need to do anything. Newer clients will be able to connect to your server with no configuration needed.