Step 2: Notches
Mark out notches that are 3/4" square. Cut them out with a hand saw and a chisel. On the molding, cut a miter for the depth of the profile, so that the molding breaks cleanly at the joint.
Since the wood was so splintery and brittle, the joints blew out some. This could largely be avoided with a router table or a table saw.
Scribe the notches from the top board to the matching legs on each side. Reverse the cuts. Everything should fit together, with the slots lining up continuously.