Place the 1- by 3-inch pieces of wood on edge, with the shorter lengths inside the longer lengths forming a 24-inch square. This apron will be the support for the table.
Drill guide holes through the longer pieces of 1- by 3-inch into the ends of the shorter pieces. You will make eight guide holes, with two at each corner where the short pieces abut the longer pieces. Place these holes 3/8-inch in from the side and at 1- and 2-inches down from the top edge of the wood.
Put a thin line of wood glue along each end of the shorter 1- by 3-inch pieces. Place the pieces back into the 24-inch square and realign the guide holes. Screw the pieces together with the wood screws.
Place the apron on the 30- by 30-inch plywood table top. Center it 3 inches from the edges and make a pencil mark all the way around it. Remove the apron and flip the plywood over.
Mark guide holes that will be used to attached the apron to the table top by using a pre-made rectangular paper template or measuring tape. Make eight guide holes -- two at each corner -- by lining up the template with one corner and making a pencil mark at the spot 6 inches up and 3 3/8-inches in. Flip the template the other direction and make a mark at 3 3/8-inches up from the edge and 6 inches in from the next corner. Repeat at each of the other corners. Drill the guide holes. Flip the plywood over to check the alignment.
Place wood glue along the top edge of the apron. Carefully align the table top with the pencil-marked side down, facing the apron. Use the already-drilled guide holes in the table top to drill into the apron. Affix the table top to the apron with your wood screws.
Mark the apron with guide holes for attaching the legs. Make a pencil line at 1 3/8-inches in from each corner in both directions. You will end up with eight lines. Make marks at 1- and 2-inches down from the top of the apron on the sides that already have screws in them, marking them evenly with the screws that are already in place. You will have eight marks. Going the opposite direction from each corner -- on the short pieces of the apron -- mark 5/8-inch and 1 1/2-inches down from the top of the apron on your 1 3/8-inch line. It is critical to mark these holes correctly to avoid other screws.
Hold a leg in place and drill the pre-marked guide holes through the apron and the leg at the same time. Repeat for each leg.
Put wood glue on the three surfaces of the leg that will touch the table. Re-align the guide holes and screw the leg in place. Repeat with the other legs.
Fill the countersunk holes with wood putty. Let dry completely.
Sand the wood putty and any rough areas of the table.
Paint or stain the table. If you use a stain you will need to seal it with a brush-on polyurethane according to the directions on the can. Seal your table after the stain has dried completely.