Create a new file and import the image you want to alter.
Cut away the background of the image and any unwanted elements. There are many ways to do this depending upon the program you use, but the most straightforward method is to use the eraser tool and erase the background. If you want the background to remain in the final image, duplicate the layer that your photo is on first. This will preserve the background for later.
Warp the area that you want to disintegrate on the image. Again, there are many methods for this depending upon the program you use. In Photoshop programs, the "displace" filter is good for this, but you must select an area of the photo to warp first. In Corel Painter programs, brushes are often capable of this, such as the distorto or turbulence brushes.
Blur the edges of the warped area to make them look more natural. Again, you can use a filter, and most programs have a suitable brush as well. Blur slightly for a natural look, and blur more strongly to make it look as though the disintegrated area is moving.
Select a color from the disintegrated area of the photo using the eyedropper tool, and then choose a hard brush. Paint in bits, flecks and dust to make it look as though pieces are actually coming off the image in a cloud of debris. Some filters will achieve a similar effect. You can also use a softer brush and curved strokes to create a dusty or smoky look. Again, you may need to blur your work to make it look more natural once you have finished.
Choose a very soft brush and brush in smoke or dust around your debris.