Can you please recommend free or inexpensive software, or a plug-in that will allow me to preview/visualize a flat 2d square image when it has been folded in half or in thirds?
Parts of the image are selected and distorted(=stkewed + scaled horizontally to smaller width) to simulate some folding. The angles are "by eye", not exact known degrees. The widths also are "by eye". Of course one can have a prepared model to follow in another layer. It shows the places of the corners (=total 8 here) before, in the middle and after the work.
Some apparent smooth curvature in the bend is simulated by making two smaller foldings with different widths.This comes easily unintentionally when one makes a tweak. The mid part is darkened a little and a shadow is drawn and blurred to the background.
Total working time = few minutes. If you can live with this kind of low level sophistication and accuracy, you will do well with Photoshop, GIMP or any other photo editor which allows layers and easy distortion of selections.
This one is crunched together in Photoshop, which is especially easy and flexible without any add-ons for transformations this simple.
There are lots of services / plug ins / pieces of software that will automatically generate a 3D visual from a piece of flat artwork, one of my favorites is http://www.psdcovers.com, but that relies on you having photoshop and being able to use it at least a little. A bit of searching will throw up many others.
The problem with the free and easy solutions is that they tend to be somewhat inflexible. If you are serious about visualizing your designs then your time would be well spent learning how to create your own visuals. This would involve use of some 3D modeling software or getting VERY good at using Illustrator, Photoshop or similar.