Electromagnetic fields contain both an electric field component, and a magnetic field component (as I imagine you know). The ratio of the electric field to the magnetic field (E/H) is known as the wave impedance, the higher the wave impedance the larger the electric component compared to the magnetic component.
A field can be purely electric or purely magnetic only if it is static.
Conductors provide shielding of electric fields and magnetic fields by different mechanisms that I will describe:
Electric fields are shielded by charge redistribution within the conductor. Static E fields can be shielded this way, charges in the shielding conductor shift to new positions and stay there when the static E field is applied.
Magnetic fields are "shielded" by two other mechanisms:
1 - Magnetic fields are shielded by inducing eddy currents in the shield conductor, and by Lenz' law the magnetic fields caused by the eddy currents cancel the incident field. However, eddy currents are only formed when magnetic field is changing. Thus static magnetic fields cannot be shielded in this way. This mechanism involves expelling magnetic field from the conductor, not allowing it to penetrate (the amount of penetration is known as skin depth).
2 - Magnetic fields can provide "shielding" by doing the opposite, deliberately enticing the magnetic field into the "shield". Shielding of low frequency magnetic fields using high permeability metals uses this method. The idea here is that the magnetic field will follow the path of lowest reluctance, which is within the high per metal, thus diverting it away from what you are trying to "shield" it from. In this case eddy currents are your enemy and methods are used to reduce them.
To your last question:
Can we shield a field 100%? You know nothing in the real world is 100% right (unless you are rounding off). Your permanent magnet emits a static magnetic field, you would need to apply the second method, high perm material around it. The permanent magnet has lines of flux connecting its poles. This flux will prefer path of least reluctance (just as electrical current prefers path of least resistance), and the high perm material provides a low reluctance path. However, the reluctance is not 0, not *all* of the flux will go through the shield. You will get closer to your 100% if the shield is a mile thick than if it is one inch thick, just depends on how close to 100% you want to get.