Sit in the back extension machine, with your back resting against the lever and your feet on one of the foot pads (foot placement is incorrect in illustration; awaiting correction).
Adjust the lever so that it pushes your torso down and allows you to get a full range of motion when you perform the exercise. The angle of your hips should be approximately 90 degrees.
Press your lower back against the lumbar support pad by pushing against the foot pad. As explained in the Comments and tips, this is important to keep your hips from extending as you extend your back.
Keeping your hips fixed, exhale as you slowly extend your back until it is slightly hyperextended.
Hold for a count of two.
Inhale as you slowly return to the starting position.
Comments and tips
To avoid back injury, keep the movement very slow and under full control.
Keep your chin and neck neutral.
The machine back extension targets your erector spinae (spinal erectors), a group of deep muscles that run up your spine and work to extend, laterally flex, and rotate it. In order for your erector spinae to be isolated during the machine back extension exercise, your hips must remain stationary, and all of the movement must be in the extension and flexion of your spine. Pressing your lower back against the lumbar support pad helps to keep your hips stationary.
Some back extension machines do not sufficiently prevent your hips from moving, in which case your gluteus maximus, hamstrings, and adductor magnus will act as synergists.