Set one 4-by-4-foot sheet of 3/4-inch furniture-grade plywood on your work table. Place a circular object such as a glass or bowl at one corner. Trace around the edge of the object that is closest to the corner of the plywood with a pencil, making a rounded cutting guide for trimming the corner into a curve. Repeat at each corner of both sheets of plywood.
Cut the plywood pieces along the rounded pencil marks with a jigsaw.
Examine both pieces of plywood, choosing the grain pattern that you prefer for the top. Place the best piece on your work table with the top facing down.
Pour a generous amount of wood glue on the plywood, and distribute it evenly with a foam paint roller.
Set the other piece of plywood on top of the first, and align the edges. If your rounded cuts are slightly crooked, only align the straight edges. You can neaten the corners later.
Fasten two clothespin-style, spring-loaded wood clamps on each side of the table edge, holding the two layers of plywood together.
Insert wood screws through the plywood with a power drill and a Phillips head bit. Space them six to eight inches apart along all four edges, at the center and across the surface of the plywood. Pre-drilling is unnecessary, and the screws are too short to pierce the other side.
Wipe off excess glue with a rag and let the tabletop dry overnight.
Remove the wood clamps from the table edges.
Choose the locations for your table legs. You can place them close to the edge of the table at each of the rounded corners, or space them a few inches in from the corners. If they are too close to the center, the table will be unstable. Mark the table leg locations with a pencil.
Center one mounting bracket top plate over a table leg location mark. Insert the screws that came with the bracket plate through the screw holes and into the tabletop with a power drill and a Phillips-head bit. Repeat for each of the four table legs. If your brackets did not come with screws, use 1-inch wood screws.
Twist the bolt at the top of the table legs into the bracket plate bolt openings, attaching the legs to the tabletop.
Stand the table on its legs.
Sand the edges of the table with a handheld power sander and medium-grit sandpaper, then change to fine and then ultrafine sandpaper. If the rounded corners are uneven, begin with coarse sandpaper to neaten the edges, then switch to finer grits.
Set an iron to the heat level required by the heat-activated wood veneer strip manufacturer.
Place one end of the wood veneer strip against the edge of the tabletop with the wood side facing out. Press the iron against the veneer and move it back and forth over a 1-foot section for the amount of time required by the manufacturer; do not keep the iron in one place, as it will burn the wood. As soon as one section is bonded, rub a block of wood back and forth across the area to help secure the bond as the glue cools. Work your way around the edge of the tabletop. Stop approximately 1 inch before you return to the starting point.
Cut off the excess veneer with a utility knife, butting the ends of the trim together. Iron the seam to make the ends of the veneer lie flat.
Trim off excess veneer around the upper and lower edges of the tabletop with a utility knife.