What tool would you use to remove a tick from the skin of a dog?

Your best option is to clearly mark the location of the tick, such as by trimming the hair around the tick, and then taking your dog to a veterinarian. Once the head of the tick is lost in the skin, it will likely take local anesthetic and possibly a bit of surgery to remove it.

Trying to remove this at home is probably just going to make the situation worse.