Do I need to do anything to my dog's fur to make sure the contact grid touches its skin?

The contact grid needs to touch your dog's skin or come very close. If your dog has an especially thick coat, you may need to trim your dog's fur to some degree around the area where SkyShepherd will sit while worn, but most dog's coats are fine to wear the collar without trimming as long is the collar is fitted properly, in accordance with the instruction manual.