Nuclear radiation is tricky because it comes in different kinds. The kind we worry most about is called ionising radiation, and includes alpha particles (charged bits of nucleus), beta particles (individual electrons), neutrons (uncharged bits of nucleus) and gamma rays (high-energy light).
The general aim in stopping ionising radiation is to give it something to hit and ionise that isn't yourself. Alpha particles can be stopped by metals, earth, enough water. They're charged, and you can also use strong electromagnetic fields to bend or deflect them. Beta particles are essentially electrons and lighter than alpha particles, so they can be stopped by a thinner layer of pretty much any of the above -- even your epidermis can stop a lot of beta radiation (and "beta burns" can make your epidermis slough away).
Neutrons are uncharged, and you want a thick layer of dense stuff to stop them. You do not normally want to use water to stop neutrons, because when neutrons hit water they tend to spray neutrons like shrapnel.
Like neutrons, gamma radiation is uncharged, and you want a thick layer of dense stuff to stop it. I'm not sure if you can play polarisation games with gamma, the way you can with visible light -- or if so, what material you'd use.
Fallout is made up of particles of radioactive dust and other heavy matter. Protective suits can help keep such dust away from you, but the real problem is that it makes its way into the food chain -- the water you drink and the food you eat. Filtering can help keep it out of drinking-water, but once it's locked into plant and animal tissue, I don't think there's much we can do other than not eat those plants or animals -- or else take medication for the effects of doing so.
Hope that helps.