Attach the Spacers
Ty used three long and three short spacers on his counter. The long ones passed through a hole in the boxes. I suspect that he did this primarily because he thought that it would look nice, and it did. But it also made for a somewhat weak, unsupported corner, and the effect was lost when the last minute decision was made to turn the counter around so that the open sides of the boxes faced the wall, rather than out into the room. With the open sides concealed, they could be used more effectively as storage (and what wet bar does not need storage?). So you will probably be better off using spacers of all the same length. Plan to use at least six spacers, two on each box, and consider using even more for added strength.
The final assembly will depend on the type of hardware or material you are using to connect the spacers to the boxes and countertop. Begin by setting the boxes in the position, exactly as you want them spaced and aligned with the final project. In most cases, the open sides should all face the rear. Check to see that the tops are all level, then drive a few screws through the walls to connect the boxes to each other.
If you are using threaded pipe with mating flanges, first attach flanges to the boxes, with one flange near the front corner and one near the back corner. Now thread the pipe into the flanges, and then attach the top flanges to the spacers. Carefully set the countertop on the flanges. When you are satisfied with the position of the countertop, drive screws through the flanges and into the countertop. If you are using fairly short spacers, you may not have much room for operating a standard screwdriver. In this case, use a short or an offset screwdriver.
With spacers that are joined other than with threaded connections, this approach will still be the easiest way to properly locate the flanges on the countertop. Some types of metal tubing can be joined to flanges with setscrews. PVC will require appropriate primer and cement. When sliding the finished counter around in the room, I suggest pushing or pulling on the boxes and not on the countertop itself.