Trim the ends of a lemon. Use a bar spoon to remove the inner of the lemon, keeping the skin whole. Slice once lengthwise so you have one wide strip of lemon peel. Using the bar spoon to remove more of the white pith, if necessary. Roll the lemon peel up tightly and thinly slice.
For the second type of zest, trim one end of the orange to stabilize. Slice off the peel in thumb-sized pieces, avoiding the pith. Trim sides to make a cleaner shape. Enjoy in a variety of drinks!