Maybe you're like me and you don't like the tough white skins on citrus fruits. So when I realized that there's an easy way to cut around them and only have the orange flesh, I was in heaven.
And it's really easy to to, just follow the steps:
Cut off the top and the bottom of the orange. Just look for the navel and the stem and cut away about 5 mm / 1/4 inch thick slices from both ends. Make sure there is no white skin left - if there is, cut away another thin slice till the cut section looks all orange.
Place the orange with a cut side down on a cutting board (with those juicy oranges it helps to have a little groove around the edge of the board). Start at the top and cut away the peel. Make kind of a semicircle movement and try to get off as much as possible of the white stuff, while leaving as much as possible of the orange stuff.
Work your way around the fruit, then take it into your hands and check for white spots.
Now look for the widest wedges, because they're the easiest starting point. Hold it in your left hand like a tennis ball (if you're a lefty, hold it in your right hand, of course), so that you see the segments and not the navels. Cut along the white walls to get out a wedge. Turn the fruit and cut out the next wedge. Continue until you have only walls left in your hand and all the citrus wedges in a bowl. If you want to, you can now squeeze the walls to get out all the juice - that's a bit of a mess.
This works for every kind of citrus, except maybe kumquats (where even I eat the peel) and buddah's hands... But I cut lemons, oranges, grapefruit that way and it's getting easier every time...