Every person within humanity can be distinguished and classified by several *relatively* indicative (but nonetheless non-unique) signs, but the truley 100% unique indicator that I find the most appealing is the ability to think abstractly. Instead of defining this term itself, I'll give you a few examples of abstract thinking. One is introspection. Humans alone are capable of introspection, which is essentially the physiological process of self reflection and examining one thoughts and feelings. Regardless of whether we can visibly notice this quality in a person, or it is extremely inconspicuous, all humans are introspective at most points in their life, and this is, as I said before, an entirely unique quality in our species. No other species examines their thoughts. Anyway, even the select individuals within our species that are considered different for one reason or another can be identified by this, if prompted correctly. Some other abstract process we demonstrate very uniquely to our species are self awareness/consciousness. However, these tie in closely with introspection. To clarify on their definitions, though, self awareness is simply our cognizance that we exist, and consciousness is more or less the same thing (I just threw in the word because it might clarify to you more what I'm talking about exactly). This is also unique to all humans and identifies them easily.
It is my duty to note, however, that as I was writing this, I realized that babies might not demonstrate some of these qualities, and after looking that up, I was right. To explicitly label a baby (under the age of 2, specifically) as human would be somewhat harder, then, in my opinion.
There are a few other thing relatively unique to our species, but not everybody shares these qualities. For example, not every human possesses the capabilities to construct complex grammatical sentences using our upper level and highly developed form of communication, or to speak with the aforementioned language, for that matter. Additionally, not everyone is part of the complex human social networks that are so evident to us. Because these qualities are exhibited in either a large number of other species or a minority of species that are decidedly non-human, they cannot be used as crystal clear, lucid signs of the humanness of an animal - although some signs can give us 99% assurance that an individual is human.
So there you go - my opinion is that humans, ALL humans (except babies under the age of two) can be identified, whether it is a difficult process or not, by determining if they have a sense of introspection, self awareness, and consciousness (all under the umbrella of abstract thought). How once can check for the existence of such abstract thought processes is another issue entirely.