With this cold getting me down, I've been trying to hit the citrus and vitamin C with full force. Then I found my knife bag after 8 months of neglect and decided to see where my knife skills were at. But mostly I wanted vitamin C.
First, slice off the top and bottom where the stems are so you have a flat bottom to rest the fruit on. It gets slippery, so always cut away from yourself. Then start from the top and shave off the rind- it will mean cutting in a curve with a gentle sawing motion. It is best to do this in eighths or even tenths. If you are losing too much meat, then shave a smaller portion. See picture below for a better idea.
Holding the fruit in your hand, VERY carefully slice between either side of the membrane, removing only the juiciest flesh. Go slowly and carefully. And make sure your knife is very sharp. You can hold the fruit in a towel if you're nervous it will slip. (Sorry, I had to photograph this one-handed.)
The cut-out membranes will start to make a little accordion, just keep going. This is crucial French pastry technique. Your friends will think you're fancy!
Enjoy, and laugh in the face of colds and flus.