Locate the "Line Out" ports on the rear or side of your karaoke machine. The location depends on the model and manufacturer of your particular machine. Plug the audio output cables connected to the TV into the audio inputs on the machine's mixer.
Plug in the microphone cord's input into the appropriately labeled input on the mixer's front face. Plug the mixer's output cord into the input port on the machine's amp, and plug the output cables running from the amp to the input ports of your speaker set.
Turn the volume levels down on the mixer. Plug in the mixer and amp's power cords into wall sockets or a power strip and turn all components on. Level up the volume to match the room where the karaoke machine is situated and make incremental volume adjustments to suit.