Connect the microphone to the mixer with an XLR cable. Connect the cable to the desired channel strip on the mixer. This allows a signal to flow from the microphone (input) to the mixer.
Connect the main output of the mixer to the input of the equalizer with a patch cable.
Connect the output of the equalizer to the amplifier with a patch cable.
Connect the left and right outputs of the amplifier to the inputs on the speakers using speaker cables.
Turn on the power to the mixer, equalizer, and amplifier with their level controls turned up. If each piece of gear is receiving levels, and the input is audible from the speakers, the hook up is complete.