Dismantling a standard Rubik's Cube can typically be performed without any tools. The ease of disassembly can be determined by how easily the cube's faces turn - a sticky or slow cube will require more force to take apart.
First step[]
The first step is to turn one face 45 degrees. Then, you can simply pry from the underside of a corner, and eventually the cubie will pop out (Do not do this in an environment where one may not be able to retrieve any far-flung objects, like a boat at sea, because they will typically fly off the cube due to the amount of force involved). One may want to use a flathead screwdriver for more leverage.
Re-assembly[]
Re-assembly should be straightforward, until all but the last layer remains. Then, put in all the other pieces except for one edge. Turn the face missing the edge 45 degrees, put the missing edge in the slot, and push downwards. (If you need detailed instructions, see How to assemble a Cube4You cube.)
Do not re-assemble your cube scrambled. This will typically create an unsolvable combination, and without re-assembly solving would be impossible. An unsolvable cube like this may be used as a practical joke, but little else.
A word of warning: Any other cubes or cube variants will follow slightly different methods of disassembly. Most will still be disassembled by turning one face 45 degrees (or the equivalent halfway angle if using a Megaminx or Pyraminx), but re-assembly or even the fundamental mechanism will change from cube to cube. Because even-numbered cubes (Pocket Cube, Rubik's Revenge) have no set centers, reassembly will be much more difficult than reassembling an odd-numbered cube.
Irregular cubes[]
Irregular cubes, also known as Cuboids, (that aren't really cubes, but square/rectangular prisms) will also be more complicated. The Floppy Cube or Rubik's Tower are good examples of this. The Void Cube is also different than a standard Cube.
Void Cube[]
Apparently, you use different methods for the Void Cube because it is centerless.