Drawing three dimensional images are difficult to create because of the inherent two dimensional nature of the drawing surface. Over years of refinement artists have found ways to depict three dimensional items in two dimensional mediums. Perspective, foreshortening, and ocular occlusion are only a few examples. Different layers or depth of an image will move less through the field of vision of an observer. This means that objects at varying distances in the image shift differently across the many layers or angles of viewing used for the individual interlaced images.
The earliest forms of 3D imagery used stereoscopy, or two separate images each from a distinct view point, to create a feeling of depth. The slight variations between each image mimic what the human eyes see. The brain is great at interpreting both images at once and thus perceiving depth. A lenticular 3D creates the same effect and because each eye has a slightly different view point to the lens the light it sees will be from a different part of the image and because the source image is interlaced that means each eye sees an entirely different image. This allows the brain to do it's job of interpreting two images at once and perceiving depth.
There are multiple ways to create each angle of the image. The easiest is to physically take an image from multiple view points which can be done by setting up multiple cameras or a system that moves a camera in standard intervals. The Mitton rail system shown in the video on a previous post is one example of this. To manually create an image form a flat surface takes a bit more manipulation the workflow for which is shown in the below video.
Yet another way to create these images is to use a rending software of a digitally created scene. Software such as Solidworks Photoworks, or Blender can be setup to have multiple camera viewing angles. Each angle can be rendered separately and then interlaced to create stunning 3D of a digital scene. Those accustomed to macros and batch processes will notice that with a few key criterion (interlacing spacing, viewing distance, number of images) are all that is needed to easily create a interlaced image for home creation for nearly any rendered scene.
For more to look for in lenticular imagery return to 3DEngr's 10 things about lenticular.