The source above is not exactly a tutorial, but it gives you a basic idea of how the author built a Quirky Pallet Art to enhance the look of their old house. You can also find another tutorial at the link below. It shares a step by step procedure for making a wooden pallet sign. The final product is not exactly the same as the one above, but the basic idea is the same.
Drill a pair of 3/8" holes in each end of the short stretchers, just over half of the depth of the dowels, using a brad-pointed bit. These stretchers already have a groove running their length, centered on the bottom edge. Precise placement isn't necessary, but keeping track of which part is which is. We need a hole in each end of each stretcher. Take care to keep these holes square, you don't want them running at angles.