Dogs, wolves, coyote and fox all instinctively track from oldest to newest scent. Any animal that hunts for food does so because if they don't, they aren't likely to eat. A fairly common newbie training mistake to make is to teach the dog to track backwards. It isn't that dogs cannot track backwards, it's just that they have a strong instinctive desire to track forwards. I think we can rule out that sort of newbie training error in the case of the FBI dogs.
Now, imagine that the dog is looking for scent and moving along a path that is perpendicular to the scent trail. The two paths make a shape like a capital T (dog's path the vertical stroke, target scent the horizontal stroke). There's a chance that the dog will initially start tracking backwards. But an experienced, well trained dog will reverse within 10 feet if they find themselves going backwards. A normal, healthy human can cover 10 feet in 1-2 seconds at a brisk walk. So that means that a dog can tell the difference between scent that is 2 hours old and scent that is 2 hours 2 seconds old.
Pretty amazing!
A very common LE task for dogs is to figure out if a certain item was placed by the target person or if that item got into the environment in some other way. So the dog will be given the target scent from an item known to have been handled by the target person. Then they take the dog to where the item was found in the environment and the handler does the equivalent of asking the dog "did the target person go anywhere after this item was left here?"
The dog will check out the item and indicate "yeah, the target person was definitely here." Then the dog starts searching to find out where the target person went next. Most dogs will start making a loose spiral centred on the item. If they can't find any newer scent, they will go back to the item and then resume casting for newer scent.
Depending on the dog, they will circle the item 1-4 times before checking back at the item. Usually by the second time the dog checks back to the item, they are giving off definite signals of "ain't no newer scent here, partner." The handler usually encourages the dog to try again but at some point, the dog makes it clear that they are simply not finding newer scent. Some dogs will bark at their handlers in a very annoyed tone, as if they were saying "what part of this are you choosing not to understand???" Dogs are willing workers and remarkably tolerant but they don't have infinite patience.
I am purely speculating here: I think that when dogs are in an environment that they perceive it very differently from humans. For a human, it would probably be like being able to see a type of ghost of everyone who had moved through that environment in the last 2-4 weeks plus seeing the solid form of anyone who is actually present in the environment.
As a general guideline, if a scent question can be phrased in such a way as to require a yes/no answer, then a dog can be trained to answer the question.
but I didn't quite get how it worked. 
