There are already a number of posts and videos online about "how to supreme an orange", but here is one more for your convenience as you're here already. Composed salads using citrus are much easier and more enjoyable to eat when the membrane is completely cut away.

Slice both ends to create a flat stable surface as well as remove peel and pith
Rotate the fruit so one of the flat ends is against the cutting board and proceed with cutting peel and pith around the entire orb; you'll be taking the back off the membrane, too, exposing the flesh. Take your time as the juicy fruit can be slippery. [Note: a sharp paring or slicing knife is better to use here rather than a (wider) chef's knife. Donald prefers to use a boning knife].
Hold the fruit in your hand, position the knife edge as close to the membrane as possible and gently slice to the core. Repeat this on the opposite side of the same segment, essentially having sliced a "V" and releasing the flesh from the membrane.
Continue to rotate the fruit and liberate each segment from its membrane. Take your time and be aware that the last segment or two are the tricky ones.
Once all segments have been removed squeeze the pulpy membrane in your hand over the slices you have captured. This is extra juice can either be added to your dressing, or can be enjoyed as as a refreshing little sip for the cook after you've placed the segments on your salad or dessert.

three panels showing how to supreme a cara cara orange

The final three panels showing how to supreme a cara cara orange

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