For running Minecraft you need to have Java (icedtea7) installed.
Obtain and run the client launcher
Download the Minecraft.jar and run the Launcher.
Sound issues when using PulseAudio
Minecraft uses OpenAL which seems to get confused sometimes (missing sounds or music), so tell it to use the pulse driver first.
Create a user for running Minecraft
Become the minecraft user so that any file you download is owned by the correct user.
Obtain and run the server binary
Download the current server binary from, e.g. minecraft_server.1.7.4.jar and run it.
Stopping the server
On the Minecraft server command-line.