Generally you arrive at an earth, with dogs, we only ever have two with us but you only ever put one dog down at any time, they are equipped with a locator collar and you have the handheld locator above ground with you.
The dog is then put down on the ground, she should go have a sniff about looking for signs a fox is there, going underground... this can take 20 minutes or much longer. You can keep track of where she is with the locator, that tells you location and depth.
Once dog had found a fox she will bark at it, and try to hold it in place (not physically) this is called baying. If there isnt a fox down there the dog should come back out fairly quickly. the dog can also bolt a fox and there should be people above ground well versed in shooting bolting foxes who can then shoot it quickly and cleanly (would be so much easier if this happened more often)
Once the dog has stopped moving about and is baying consistently then you dig down to it, the dog shouldnt have touched fox and should have kept a distance between them.. obviously they are anmals and scraps can occur, but they are rarely to the extent PaulT described.
Once you have ''broken though' to the tunnel you should be above the distance between the dog and fox, fox can be grabbed and pulled out and then dispatched, or if the shot is viable and sure of a safe kill then it will be shot in the hole.
It may sound very traumatic, but i have witnessed foxes bolt out of the hole and literally trot off completely nonplussed.
Hope this helps..