Slice the oranges thinly with a sharp knife. Lay the slices onto a parchment-paper lined baking sheet or dehydrator tray.
3 oranges
If using an oven, bake the slices at 200°F (90°C) for 2-3 hours, or until fully dry. Flip the oranges every 30 minutes and move them around as the oven or baking sheet might have hot spots. Take the individual slices off the sheet as they dry to prevent browning.
To use a dehydrator, dry the slices on the lowest setting for 12-24 hours. You don't really need to worry about discolouring or browning if using a dehydrator.
The oranges need to be fully dried, not gummy or sticky at all. Once dry, use a needle to string the thread through in any way you'd like. The garland should last months if kept in a cool, dry place.
Notes
3 oranges is a good starting point, and you'll get a garland long enough to use for most windows and doors.