Step 2: Groovin'
For maximum strength, I routed some grooves that allowed the legs to notch into the top and vice versa. This eliminates some of the weaker end-grain mechanical connections in the previous design, provides a cleaner finished appearance, and minimizes the number of store-bought fasteners needed. These joints are very simple, and, if built tightly, extremely strong.
I used a plunge router with flush-trim bit. This type of bit has a smooth piece at the top of it, the same diameter as the cutting part of the bit, that acts as a guide. By clamping some scrap lumber to your workpiece, you can create an extremely precise template.
Find the center of your top, then measure 18" off of the centerline to either side. Now measure a further 1-1/2" to each side. This will be the width of the notch that accepts the legs. Line up a piece of 1/2"-thick scrap on either side of your future groove. Screw or clamp down to the workpiece. Set the depth of the router to cut roughly halfway through the depth of the workpiece. Turn it on and draw it toward you in slow, even strokes, making sure the smooth part of the bit is riding tight to your guide board. Once done, sand out any router marks in the groove to even it up.
If you don't have a router, you can use a circular saw to do the same thing, albeit a little less cleanly. Set the depth of the blade down to 3/4" and make a series of passes with the saw right next to one another between your marks. Break out the chips and clean up with a chisel and sandpaper.