These directions show how to make these with a power drill, a circular saw, a hand saw, and chisels. It could be done faster, with more accuracy, if you have access to a table saw, or better, a router table. But, these simpler tools are more widely available, so you can build this in your basement or on your deck.
Your salvaged wood may be different, so dimensions are approximate.
Step 1: Cuts
To make sure the ends were square and flat, use a square to bring a perpendicular line off the back of the wood. Measure 1-1/2" off that line, and clamped a piece of wood down to serve as a fence for the circular saw.
Cut three pieces for each table: two at 24" (legs of larger table), one at 48" (top of larger table), two at 18" (legs of smaller table), and one at 36" (top of smaller table.)
These tables could be of variable dimension; these two make a side table and a coffee table. You could make a third or fourth as well. Different configurations could be used as display table, stereo stand, buffets, or, as nested, space for a flat screen with a dvd player and cable box on the lower one.
For the larger table, measure a center line onto the longest board from end to end. From that center line, make a cut 3/8" from each side of that center and 12" long, to make a 3/4" slot into the board. Use a 3/4" drill bit to round off the end of the cuts. Repeat at the other end. Do the same on each of the two smaller boards, from only one edge, taking care to orient the slots so that the molding will be unbroken all the way around the front of the finished table.
Repeat for the smaller table, but make the slots 6" long.
Step 2: Notches
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.
Step 3: Assembly
Screw one end of the threaded rod through the top piece with visegrips.
Slather up the finger joints with wood glue, and some dabs of urethane glue (like Gorilla glue), which will expand in the presence of moisture to fill the voids and gaps in the joints. Clamp end-to-end. A spreader may be needed at the feet, as they will have a tendency to lean inwards.
Screw the rod through the hole in the leg. Lock the threads at each junction by working some urethane glue into the holes.
You may or may not want to glue a little beveled strip on the inside of the joint for extra strength.
Step 4: Finishing
I puttied the holes and joints with a contrasting wood patch material to highlight the scars in the wood instead of trying to hide them.
Sand the wood heavily to smooth everything out, shine the ends of the rods, and remove any glue or dirt. Polyurethane with at least two coats, sanding lightly in between. Last, a coat of clear carnauba furniture paste wax brings up some luster and depth.