Treat each type of peel separately (i.e. don't mix fruits, handle oranges separately from grapefruit, etc.)

Using a sharp vegetable peeler (or sharp knife), carefully peel the entire fruit from pole to pole, making sure you include some of the white pith under the skin. You don't want a thick layer of pith, but approximately ⅛ inch (maybe slightly more) is perfect. Slice the peels into strips between about 1/8" and 1/4* inches wide. Put the peels into a 3-quart saucepan and add enough water to cover the peels; bring to a boil over high heat and blanch for about 5 minutes.

Drain the peels and repeat the blanching process two more times for at least 5 minutes at a full boil for each for a total of 3 blanchings.

In the same saucepan, combine 1-½ cup of the sugar and 1-cup water; bring to a boil over high heat and stir until the sugar dissolves completely. Add the peels and reduce the heat to low.

Let the peels simmer very gently - the mixture should be just slightly bubbling - until they begin to look translucent, usually about 45 - 60 minutes, but don't be surprised if they take quite a bit longer. If needed, add enough water to replace that lost to evaporation but without diluting the mixture of sugar and water.

Stir occasionally to ensure that the peels candy evenly and don't burn.

Drain the peels reserving the syrup for another use or discard it.

Set a rack over a parchment-lined or foil-lined rimmed baking sheet. Put the remaining 1-cup sugar in a bowl. Roll and toss the peels in the sugar until nicely coated, then shake them vigorously in a sieve to remove the excess sugar, and spread them over the rack. Let dry for 5 or 6 hours or over night until fully dry. Once fully dry store the candied peels in an airtight container in a cool dry place for up to a month. They can be frozen for longer storage if sealed in an air and moisture free container.