Stand two of the 4-by-4 posts up on their ends and lay one of the 1 inch by 4 inch boards across the tops, with the posts right on the ends. Predrill four evenly spaced holes through the top board and into each post. Attach the boards using the 3-inch wood screws. Repeat for the other set of posts.
Assemble the tabletop upside down on the work surface. Arrange all boards in their intended order so that there are no gaps or spaces. Lay the four 1/2-inch by 4-inch boards evenly spaced across them and screw these boards to each tabletop board using two 1-inch wood screws.
Flip the post assemblies over and set them evenly spaced on the underside of the tabletop. Predrill eight holes through each set of posts into the tabletop, taking great care not to puncture the tabletop surface. Attach the posts to the tabletop using the 1 1/2-inch wood screws.
Flip the table right side up and fill any holes or open spaces in the tabletop with the clear-drying caulk. Allow time for the caulk to dry and then coat the entire tabletop with a coat of sealant. Allow two hours for the sealant to dry then apply another coat. Repeat the process for four or five coats due to the heavy use most dining tables receive.