If you do not have a food processor, you can use your knife skills here. That said, a food processor will make this immensely easier.
Place cranberries in the food processor; pulse gently until coarsely chopped. You want the relish to have texture. Remove and place into large bowl.
Pulse the celery until coarsely chopped. Add to bowl with cranberries.
Pulse the Granny Smith apple until coarsely chopped. Add to bowl with cranberries and celery.
Pulse the orange 2-3 times or until chopped. Be gentle with the orange, as it is softer than previous ingredients. Add the orange to the bowl with cranberries, apple, and celery.
Add sugar to the cranberries, celery, apple, and orange. Stir until fully mixed and combined. Cover + refrigerate for a minimum of one hour.
Serve as a topping to your favorite holiday meat, such as ham or turkey.