One of definitions of “consciousness” is “set of phenomena” (as in perception, conscious experiences, first-person point of view).
Since it's completely unclear what that might even be from a third-person point of view on it, it's practically impossible to explain with any warranty (or, more precisely, certainty) of the explanation being understood correctly.
Additionally, there are at least 3 distinct meanings that match this definition.
It is related to the fact that one has only subjective perception of the world (“‘Objective’ (‘material’) world is given only through subjective experiences”). For understanding that, ideas of solipsism, “brain in a jar” (or, more widely known, The Matrix) might be helpful.
Also, ideas of understanding the world as set of phenomena are elaborately described in Husserl's idea of phenomenology, but they are described unclearly and might be just as hard to understand properly.
Regarding others (other people in particular), there are only two things that suggest they might have consciousness:
Additional problem with consciousness is that it didn't matter — yet.
A predicted topic where it suddenly becomes important is mind uploading, and, because of that, cryonics. But just as important it is, it's hard to make any conclusions — whether you will perceive yourself uploaded or will cease having any phenomena i.e. die. This is also known as the duplicates paradox; unclear but related is the mind/body problem.
Given the duplicates paradox, the practical problem of uploading is finding out what consciousness is from the third-person perspective, i.e. finding neural correlate of it.
Given aforementioned phenomenal judgments, it might be treated as an unsolved scientific problem.