Data Structures
The simplest way to store voxels is to define a three-dimensional array of elements (be it structs or integers), where each element represents a single voxel:
int width = ...;
int height = ...;
int depth = ...;
var voxels = new VOXEL[width][height][depth];
// Set a voxel:
voxels[x][y][z] = voxel;
// Get a voxel:
var voxel = voxels[x][y][z];
However, because storing arrays within arrays often means having pointers pointing at pointers (which ain't good for various reasons we won't get into here), it is generally recommended to use a one-dimensional array with a clearly defined spatial indexing scheme.
Here's an example:
--snip--
// Spatial Indexing Scheme is: Y-height, Z-depth, X-width
// The arrays size is just all axes multiplied together:
var voxels = new VOXEL[height * depth * width];
// Our Indexing Formula is the indexing scheme in reverse,
// with the components being multiplied subsequently:
// x + z*width + y*width*depth
// So let's define a function (here a lambda) for it:
var idx = (int x, int y, int z) => (x + z*width + y*width*depth);
// ^ NOTE: You may want to throw an error right here
// if either the coordinate components
// or the resulting index are out of bounds.
// Set a voxel:
voxels[idx(x,y,z)] = voxel;
// Get a voxel:
var voxel = voxels[idx(x,y,z)];
Now, storing voxels in a plain array like this is perfectly fine for small scenes...
However, for larger scenes, we'll have to use a data-structure that allows both loading and purging parts of our volume (called Chunks or Bricks) from memory, nearly in realtime, without slowing down the access times of our voxel data too much.
Note: These techniques can often be combined.