Someone recently mentioned that they hated cutting up oranges for a salad because it took so long. I remember when I used to think the same thing, because I would peel the orange first, then try to get the membrane off, etc. Somewhere along the way I learned this easy way of segmenting oranges. It is so quick you can segment 2 or 3 oranges in less than 5 minutes. Hope this helps someone who doesn't know this method.
You begin by slicing both ends off an orange. You want to get all of the skin and pith. Using a serrated knife is much easier. Then set the orange on one of the flat sides you just cut, and begin to slice off sections of the peel. Just follow the curve of the orange. You want to again get the peel and the white membranes. Complete this all the way around the orange.
Next, take your knife and place it just inside one of the membranes. Slice through to the center. Next place the knife on the other side of the membrane and do the same thing. With your next cut, you'll have your first segment.
Continue around the entire orange like this. You will be left with the membranes only. Squeeze that over a bowl to get the juice. If your orange is really juicy, cut the segments out over a bowl so that you'll capture the juices. If you're segmenting for a salad, the juice is good to use in your salad dressing (in a small food processor, pulse together orange juice, champagne vinegar, small amount of dijon mustard, salt and pepper, and shallot if you want. Drizzle the olive oil in slowly (through the holes in the top of the lid if yours has them) until emulsified. I use about 1/3 to 1/4 parts vinegar to oil.)
You're left with beautiful segments in just a few minutes. If you want slices rather than segments, then after you've cut off the peel, then just slice across instead of segmenting.