Connect the AC adapter from your headphone amplifier to an electrical outlet. This is necessary because most headphone amplifiers require additional power to reach ideal volume.
Connect the 1/4-inch (TS) cable to an auxiliary/monitor output on your mixer. Auxiliary/monitor outputs are different from the main output and are best with a headphone amp to increase mixing/monitoring capabilities through your headphones.
Connect the opposite end of the 1/4-inch cable to the input of the headphone amp. Headphone amps only use a single cable because it only outputs sound in mono.
Plug in your headphones to any available output jack/connector on your headphone amp. Depending on the make or model there may be multiple connectors; they will either be labeled as outputs or they may be numbered.