Shielding

Electric fields and high-frequency electromagnetic radiation

Common forms include light and microwaves. Most information, nowadays, is sent via high-frequency electromagnetic radiation. They are blocked by covering an area in continuous conductive material, with no holes or gaps of any sort, not even seams. Spaces shielded in this way are used industrially to protect sensitive equipment.
EMC Consulting published a paper on shielding a room with aluminum foil at http://www.emcconsultinginc.com/docs/foilroom_full.rep.pdf . They found that a single layer of foil is very effective, but that the tiny seams between the foil layers create a lot of leakage by increasing the overall impedance of the structure. Following is my current plan for shielding a room with aluminum foil:
1. Construct a frame that is solid enough for you to provide a lot of pressure at the edges of the foil layers with harming the frame.
2. DO NOT purchase non-stick aluminum foil. It is coated in a way that will prevent it from connecting to the other layers.
3. Secure the foil to the frame in long single strips, using glue, staples, or tape. As few seams, folds, and bends are desired as possible -- use as large sheets as manageable, keeping them completely smooth, completely flat. The shiny side of the foil will make a better connection than the dull side, and should be placed outwards for the first layer. Create the first layer in spaced strips, leaving room between each strip for another strip to be placed over to connect them. Then place the connecting strips, shiny side inwards, such that the shiny sides of the foil mate at the seams. Be sure to allow no glue between these seams. Close the seams by pressuring tape very tightly, to ensure there are no tiny gaps, or by using staples which are placed very close together. A simple door consists of a small subsection of frame which is covered in foil and may be pressed tightly against an opening, and simply held in place by pressure. More advanced doors may be purchased from various sources.
If you have metal plates rather than foil, you can solder or weld them together, which will give more effective shielding more rapidly than foil. Leave no gaps in any of the joints, providing a complete connection between all edges. The solder joints or welds provide excellent conductivity for electric shielding. A commonly available metal plate is steel, which has less electric shielding compared to aluminum or copper, but will offer magnetic shielding as well.
Test your room by seeing if your cell phone works in there, or if you can get wifi. If either of these function, you definitely need to close any small gaps, or make another space or another layer inside the one you just made.

Magnetic fields and low-frequency electromagnetic radiation

A common form is AC power. Shielding from these signals is more difficulty and may involve a magnetic metal such as iron or steel. Researchers use strong magnetically shielded rooms to study the magnetic fields produced by the human brain, but in general it is more common to use and study the electric fields.
On Jeremy Radlow's old page, he mentioned the approach of mixing iron filings with paint in order to provide shielding which would include some protection against magnetic fields. I might imagine alternating layers of such paint with strong electric field shielding between them. Insulation such as normal paint should be placed between the layers, so that the iron filings do not disturb the smooth surface of the electric shielding.

Physical vibrations

Common forms are sound, ultrasound, projectiles, earthquakes. These are blocked as sound would be. My personal experience is that building layers of electric and magnetic shielding ends up also providing a lot of sound shielding, inadvertently.

All of these transmission mediums share the attribute that high frequencies can store a lot of data and be directed very precisely, but cannot penetrate through a lot of material, whereas low frequencies cannot hold a lot of data, cannot be pointed or directed very well at all, but also will travel through most things. We commonly use the "sweet spots" of medium-range frequencies that can be both distant and precise in order to transmit information already -- for example microwaves, light, and sound.

To learn more, pursue classes in physics, electronics engineering, and electromagnetic compatibility. Classes, both free and paid, may be found around in the internet (links?). Please do study these things, get involved for the long haul, and share your work and education. Otherwise how will we move forward?

Although gasses, particle radiation, and nanomachines could also enter a secure space, these are not the problems to begin looking for. First secure against things which are reasonable threats. Then worry about obscure things, which are much, much harder to make use of.