How to install fabric carpet on a (remote) server

To set up a 1.14+ Fabric server (with the Carpet mod):

• Download the Fabric installer from https://fabricmc.net/use
• Download a clean vanilla server jar for the MC version you are using from https://mcversions.net/
• Create a directory for your server, and put both of the files from above there
• Run the Fabric installer, click on the Server tab, and click on Install.
• Either name the vanilla server jar server.jar, or in a file called fabric-server-launcher.properties give the name of the vanilla server jar, like so: serverJar=minecraft_server_1.14.4.jar
• Run the server once. On first launch it will close because you need to accept the EULA (unless you copied/created that file before hand).
• In the eula.txt file, set eula=true.
• Also edit the server.properties file to your needs (seed, generator settings, difficulty, etc.) before the world gets generated.
• Put the Carpet mod jar file (and any other Fabric mods you want to use) into the mods/ directory.
• Start the server for example using the command java -Xms1G -Xmx4G -jar fabric-server-launch.jar nogui
• To stop the server, run the stop command in the server console.

Remote server

You need to upload the files and dirs marked in red for Fabric itself, and then you obviously want the ones marked in blue for vanilla, and the ones marked in pink may need to be renamed and the properties file edited to point to the vanilla server jar, depending on your hosting solutions and software and how it selects the jar to launch.

So basically you want your server panel or whatever to launch the server using the fabric-server-launch.jar, either by selecting it/inputting the name somewhere in the launch settings, or by renaming it to the name your server panel expects the jar to be named.

And then you need to tell that fabric launcher where the vanilla jar is, by editing the fabric-server-launcher.properties file to have the name of the vanilla server jar.