How would I identify a set of coordinates (x, y, z) to be in which octant in a 3d space? Is it just based on the x-value? Depending on the x-value (1-8) used?

Answer 1

1,1,1
1,1,-1
1,-1,1
1,-1,1
-1,1,1
-1,1,-1
-1,-1,1
-1,-1,-1
are all in different octants
you need the sign of x y and z.
They are called octants because there are 8 of them.
Draw a picture.

Answer 2

Like here:
http://en.wikipedia.org/wiki/Octant_(solid_geometry)