Preheat your oven to 170F.
Using a sharp knife, slice each orange into 1/4 inch thick slices. Don't worry about measuring them with a ruler or anything, just do your best to keep them thin and as even as possible.
Blot each side with a paper towel or dark kitchen towel (that won't show stains) to remove excess moisture and speed the drying process. I usually toss all the slices on a towel as I'm cutting, then toss another towel on top and blot them all at once.
Line your baking sheet with some parchment paper and lay the slices on the tray, making sure there's room between each one. If you can fit two baking sheets in your oven and have enough oranges, keep going until you have both filled.
Place the baking sheet (or sheets) in the oven and dry for around six hours. Flip them every hour or so to keep the edges from curling up. Around the 4.5-5 hour mark, start checking to see if any of the oranges are done. If they are, remove them and set them aside. Continue this process until all the orange slices are dried.
Once your orange slices are completely dry, you can store them in a pretty jar and put them on display, make them into Christmas decorations, garlands, etc. If you want to use them as drink garnishes, store them in an airtight container in a cool dry area until you're ready to use them.