Joining The Cabinets Together:
First thing, for our sideboard project I went with 2 unfinished upper cabinets from Home Depot. This was the cheaper option than buying a pre-made sideboard.
Once the cabinets are lined up and level take your 1 1/4 inch wood screws and drill into the side of one cabinet into the next. You want to drill into where you have your shims that way it joins the two cabinets together.
Take your 1×3 pine board, trim it down so you have a piece in all four corners. I just trimmed two pieces to fit in snug on each end. Make sure you wood glue the boards in, then secure with your 2 inch finish nails.
For the center of the cabinet I just trimmed smaller pieces to go on either side of the center, that way I could install one leg in the center of the cabinet.