This exercise is a machine variation of the squat. Depending on the machine available at your gym it may be performed in an upright or at an angled position. This is nowhere near as effective as the free weight squat as it does not involve balancing the weight or incorporate as many secondary muscles in the movement.
Hack Squats primarily target the quadriceps, and secondary muscles involved in this exercise are the gluteus and hamstrings.
To perform hack squats select a suitable weight and then stand on the platform with your feet a little wider than shoulder width apart. Your feet should be facing directly forward or slightly outwards. Do not face your feet inwards otherwise you will be putting way too much pressure on your knee joints and this will definitely lead to injuries.
Lean back into the machine with your shoulders firmly planted underneath the pads. Unlock the safety lever and with your heels firmly planted on the platform bend down as far as you can as if you were about to sit in a chair. Go down as deep as you can and then using your quadriceps drive up back to you starting position with your heels still firmly planted on the platform.
Once you have completed the exercise make sure you lock the safety lever back in place.