Electric fields are easily screened. Anything that is even slightly conducting will have a screening effect. That is why houses screen the field inside them and trees, fences etc can provide screening as well, as they are all sufficiently conducting for this purpose. Metal, of course, is a good conductor and provides excellent screening. The electric field inside a closed metal box is basically zero. This is called a Faraday Cage. In practice, electric field screens are an approximation to this closed box. If the screen is grounded, the earth itself is included in the screen.
Magnetic fields are much harder to screen. There are two ways of doing it. One is to use “high permeability” alloys. The best known of these is mu-metal, but this is expensive and difficult to work with. The other is to use a conducting screen such as aluminium. The magnetic field induces currents in this which generate their own magnetic field which partially cancels the original field. But this usually requires quite thick metal plates to be effective.
Various firms offer screening services. We do not endorse any particular firm, but if you are interested, you could contact:
Field Management Services
See also specifically screening of high-voltage underground cables