There are several ways to add that shelf, most take some expertise in woodworking/furniture making/joinery. I can guarantee that example does not use brackets. It probably is done with a combination of notch and dowel in each leg and is machined with jigs to get everything to line up seamlessly.

You could use screw on L brackets, but those would look pretty amateurish. A better method would be to fit the corners of the shelf to mate with the legs(as in the example) and use Kreg screws to secure the shelf corner to each leg. You would need a Kreg jig and the proper length screws.

Or, if the end result would be painted, fit the shelf corners to the legs and drill holes from the outside of each leg into the shelf and glue long dowels in place, Leave the dowels ends proud of the leg, sand smooth primer and paint. You would need to make the holes as straight as possible. This method would be the least expensive as far as buying tools as long as you have a drill and hammer. You would only need to buy a drill bit sized for the dowels, and some way to drill/machine the corners. A Forstner bit of the same diameter as the leg(at the point where the shelf will sit) would so that, but that needs to be done in a drill press with the shelf secured to the drill press table. If a friend/neighbor has a drill press, those two bits(for the dowel and the Forstner) would cost about $15-$20. Hardwood dowels come in all lengths and would cost a couple bucks. You would drill the dowel holes in the shelf as deep as the leg is in diameter and glue in place.

You can get a low-end pocket hole jig for $20. That, and 4 screws would have you on your way.Or get a step up with screws and other accessories for $27

Excellent write up Mac.

Thanks, I appreciate that!