After doing some research and picking up two pallets from a local business we got to work. I am an inexperienced and imprecise builder, but this turned out to be an easy, fun project that is getting a lot of use from the kids. The entire kitchen is constructed from two pallets, a couple extra 2X4s we had lying around, hooks and screws, a hammer for hammering apart the pallet, drill, tape measure, and a hand saw or jigsaw for sawing the boards. We used one pallet as the back and hammered apart the second one to use the individual boards for the shelves and counter area. I had a general plan before starting, but as we progressed we added and built as inspiration struck. Upon completion I gave the whole thing a coat of waterproofer and then we hit the local second-hand store in order to collect the necessary kitchen supplies.
The kids ended up doing most of the construction themselves, including drilling the holes.
The kitchen in its new home in the children's play area, with an unlimited supply of cooking ingredients!