Left and Right-handed fermions 
*

*Is there a simple intuitive way to understand the difference between left-handed and right-handed fermions (electrons say)? 

*How to experimentally distinguish between them?

 A: This post helicity-chirality-mass-and-the-higgs in quantumdiaries is very interesting
and I think that it offers the explanation you seek, with nice graphics.
Lubos Motl blog post (more technical viewpoint on this subject)
(both posts are cross linked)
A: Examples of devices used to measure electron helicity (the current polarization state, not the handedness) are the Møller Polarimeter (which uses e.g. an Iron target where the spins of the iron atoms are aligned using an external magnetic field) and the Compton polarimeter (which uses a polarized laser beam, i.e. photons as scattering partners).
The helicity measurement works by scattering the electrons off another polarized particle (i.e. with well known polarization) and exploting the fact that the interaction rate (cross section) depends on the helicity of the electron.
The (electron) neutrino helicity was experimentally measured with the Goldhaber Experiment (there seems to be only a German version of this wikipedia article).
A: For the first question, no there can be no such general rule. The reason is the same why there is no intuitive way to understand the difference between your right and left shoe -- they are just reflections of each other but neither one is more fundamental (assuming you are not a pirate).
In other words, all the difference (that really matters) comes from the given theory. If the theory is $P$-symmetric (such as electromagnetism) you have no way to distinguish between these (that's why you haven't heard anyone talking about right- or left-handed electrons in the classical physics courses; there were just electrons). On the other hand, if the theory violates $P$-symmetry you have a chance since one type of particles will interact differently than the other. E.g. weak interactions violate the $P$-symmetry so that only left-handed electrons and left-handed neutrinos can form a weak isospin doublet (and so can right-handed antiparticles).
I will leave the experimental part of the question to someone more educated on these matters. But e.g. for neutrinos you might be able to measure helicity (which is as good as chirality since neutrinos are almost massless) which is a projection of spin on to the momentum. You know the momentum direction (since you know where the collision happened and where you registered the particle) and I suppose there are standard methods for measuring spin projection to arbitrary direction (but I admit complete ignorance on these experimental matters).
