How can the 'spin' of a particle point in the opposite direction of its magnetic moment? I am trying to understand the concept of a particle's magnetic moment being 'positive' or 'negative'...
From what I understand, a negative magnetic moment means the particle's inherent 'spin' is pointing in the opposite direction of its magnetic moment... But what does that mean in terms of 'observable' properties?
Quantum 'spin' was discovered by Stern and Gerlach when they discovered that particles have an inherent magnetic moment, so... A particle's spin IS, first and foremost, it's magnetic moment...
Edit: P.S: How does this apply to neutrons, which are chargeless, yet have a 'negative' magnetic moment?  How can it be 'antiparallel', as compared to the proton?
So, how can a particle have a 'direction' to its magnetic moment in the first place, and how can it be opposite to its inherent angular momentum (spin)?
 A: Suppose your "particle" is actually a positively-charged sphere. Spin the sphere about some axis and the moving charges generate a magnetic field. You can use the Biot-Savart law to figure out that the direction of the magnetic field along the rotation axis will be parallel to the angular momentum.
Switch to a negatively-charged sphere, and you reverse the relationship between the direction of rotation and the direction of the current. For a negatively-charged rotating sphere, the magnetic field along the axis of rotation is antiparallel to the angular momentum vector. That's what we mean when we say that a particle has a negative magnetic moment.
(A "rotating charged sphere" is not a very good model for a quantum-mechanical spinor, but it works in this case.)
A: If a spinning body has an equal amount of positive and negative charge --- so that total charge  zero --- and  the negative charge is further from the rotation axis than the positive charge, then the resulting magentic moment points  in the opposite direction to the spin.
