How to block neutrons What is a good way to block neutrons and what is the mechanism that allows this? It's my understanding that polyethylene is somewhat effective. Why?
 A: Being bulk neutral neutrons participate only weakly in electromagnetic interactions which is the dominate interaction for charged particles.
Instead neutron scattering can be thought of as primarily a contact interaction with the nuclei of atoms in the way. Light atoms (and hydrogen in particular) 


*

*have a larger cross-sectional area per nucleon than heavy ones

*take up more of the energy of the interaction in recoil than heavy ones


making them much more effective at reducing the kinetic energy of non-thermal neutrons per unit areal mass density.
Historically waxes, water and plastics have been the neutron shielding materials of choice, though concrete  or rammed earth are cheap and not too bad.
Once down to thermal energies neutrons get as much kinetic energy as they lose on average and you just have to wait for them to decay or capture.
Doping your absorber with boron, chlorine or even gadolinium will help to capture the thermalized neutrons faster. PVC gets you the chlorine for free in your plastic, and boron can be added easily to concrete or to a number of plastics.

It should not be overlooked that it takes a lot of space to slow, thermalize and capture neutrons (that contact interaction thing means they go through more material before interacting than charged particles); especially if you need to get them all. They are notorious for penetrating large quantities of shielding, and distance is one of your best friends when it comes to neutron shielding.
A: Depending on the velocity of the neutron one can combine different materials to shield neutron radiation. 
Diagrams for common materials can be found in The ILL Neutron Data Booklet, 4-2.1 (Download PDF 9 MB)
The strategy is to use
dense material => collisions
hydrogen as moderator => makes neutrons slower
absorbers like B,B10,Cd => captures the neutron (slower ones are easy to catch)
lead and heavy concrete => shields gamma rays too

Hydrogen in polyethylene decreases the velocity of neutrons. 
Polyethylene is usually mixed with boron as in Borotron(R).
Boron is a very good neutron absorber. Shutters at neutron beam lines are made from boron carbide with B10.
Cadmium is an efficient neutron absorber too, but it emits intensive gamma rays [Motz, Phys. Rev. B 104, 1353]. 
A: To expand on dmckee's answer, water is an excellent way to both slow and block neutrons. If you are doing any home experiments with any type of radiation, remember that the human body is mostly water and radiation will happily dump energy into YOU. Be very very careful and protect yourself. Better yet, seek the help of a trained professional or just don't do it.
