Remove both the top and bottom from the citrus.
Position a standard, sharp kitchen knife just to the inside of the orange rind, where the flesh meets the skin. It is important to cut off as much of the bitter-tasting colored flesh (called pith) as possible. You do no want to allow any of the white pith to stay on the flesh, but you also do not want to cut away too much of the flesh itself.
Slice down, following the curve of the citrus to remove as much pith as possible while maintaining the round shape of the citrus.
Clean off any pith that you see attached to the outside of the citrus.
Remove the strings of white pith from the inside of the citrus by inserting a knife just on the inside of a pith line. Cut into the citrus, following the line of pith almost halfway through the citrus.
Then, find the line of pith that is holding the slice you are working. Being careful not to slice through the pith itself, cut inside that line of pith and remove a pith-free triangular piece of fruit.
Continue this process of removing slices of pith-free citrus from the fruit until there is no more fruit to cut. Peel back and hold each pith flap out way as you go.
When you are done removing slices of citrus, squeeze the juices from the pith into a bowl.
Enjoy your sections of oranges.