These two quick steps will help you peel even the most difficult of the citrus family.
I've had only one orange in memory that didn't work this way, so it is 99 44/100% pure, oh wait that's soap. Well it works...
Slice off the top little bit of the orange (I'll use orange generically here from now on), where it previously attached to the tree.
Score around the whole perimeter of the fruit. It should have lines at what would be 12 and 6 on a clock.
Score around the perimeter of the fruit at what would be 3 finishing at what would be 9 o'clock.
Dig your thumb into the top and slide down between the peel and orange. Do that same thing three more times.
Now you are ready for sectioning. And if you really love someone you'll section a grapefruit AND remove all of the pith and membrane so that your true love can enjoy all the juicy fruit without the work.