Section the oranges and grapefruit by cutting both the blossom and stem ends off so it will stand flat on your cutting board. Then, cutting from top to bottom, cut the bitter white pith from the pulp. You will be cutting downward repeatedly, cutting away strips of pith all the way around the fruit. Next, holding the now-naked orange in your hand and over a bowl, carefully cut against each membrane to release the segments. Squeeze remaining juice into the bowl before throwing the membrane mess away.