-First, I verified that there were no wires or other obstructions, dangerous or otherwise, as well as finding the center point between two vertical studs.
-Then I measured my dog to create a hole height and width that would be as small as I could get away with. Comet easily enters and exits, but has to crouch down just a bit, which adds to the fun and mystery of the space. I then drew this shape on the wall. I created a template for half of the shape and flipped it to mirror the other half for symmetry.
-Then I began to cut into the drywall with a utility knife for a clean cut. This could also be accomplished with a drywall saw with a little more mess. Once you have the hole removed, push any insulation out of the way or remove. You can then match the shape on the interior of the other side of the wall to trace the shape and cut that hole as well.
-You will have to remove the floor tracking or stud. In my case, a 2x4 that I carefully sawed out. This can be a bit tricky, but not nearly impossible.
-Your hole should now be fully cleared and you can test it out with your dog in case you need to make any adjustments. To finish out the hole shape, I taped and mudded the drywall around the edge to create a finished look, which was painted. I also added floor laquer to the now exposed area where the wall was.
-The last finishing touch, is to line the exposed hole. I used a measured strip of 1/8" black Sintra brand plastic (PVC foam board), but a variety of flexible materials could be used. I measured the required length with cardboard and the finished plastic is simply wedged into place.
This project could be accomplished with other living arrangements as well. If the only access is the closet door, a hole could be cut in the door to allow you to close the door but maintain access to the pet-cave. My dog had already "moved in" to the space, so it was not hard to introduce the new access to him. Within a day he was using it regularly. Obviously if you have to force your pet to use the hole, you may find that they are very reluctant to use it in the future.