To prepare salad: Trim the fennel by cutting off the tall stalks where they begin to turn green.* Cut the fennel bulbs in half and then, starting from the base of the bulb, thinly slice. Place all sliced fennel into a large bowl.
Section the oranges by cutting off the skin, then use a paring knife to slice each orange segment out. Place segments into the bowl with the fennel.
Remove sprigs from the dill stalk and roughly chop. Add to the salad, then add red onion. Cover in dressing and marinate for 24 hours.
To prepare dressing: Measure out the olive oil and then season with salt and pepper. Slowly pour in vinegar, whisking continuously. Then gradually whisk in orange juice. There should be enough marinade to cover ½ to ¾ of the salad. If not, make more dressing and add to the salad.
* Fennel stalks can be eaten but are very tough. If you want, save the stalks to add a lovely flavor to broths or soups later.