Lay your chosen table top material – 3/4-plywood or a solid wood sheet – flat on the work surface.
Trace on the elliptical shape you want for the coffee table. An ellipse is oval-like or egg-like, but can be long and thin or short and rotund, or any combination thereof. If you don't have a template or an ellipse you can trace, you can create an ellipse with two pins, some string and a pencil.
Stick the two pins along the center line of the plywood, about 6 to 8 inches closer together than you want the ends of the ellipse to be. Tie a loop of string that is long enough to go from one pin to the other and about 3 to 4 inches more. Place the loop over both pins, then place a pencil inside the loop and pull the pencil out so the string is stretched. Gently move the pencil around the two pins with the tip tracing on the plywood, keeping the string stretched at all times. This will create an ellipse. See the resources section for a visual demonstration.
Cut out the tabletop shape with a band saw, cutting just outside the line, but not exactly on the line. Bring the tabletop to the exact shape by sanding back to the line with a sanding block after you’ve cut out the ellipse.
Sand the tabletop with medium-grit sandpaper, then choose a side for the top of the tabletop and sand it satin smooth with fine-grit sandpaper.
Finish the tabletop with the desired finish, whether that is paint, varnish, stain or lacquer. Follow the finish manufacturer's application and safety instructions.
Turn the tabletop wrong side up and position four plate mounted coffee table legs on the underside of the table top. Roughly 5 to 6 inches in from the edges and closer toward the ends of the ellipsis rather than the middle is good for leg positioning. The plate mounts on the legs should be flat on the underside of the table.
Secure the legs to the underside of the table with screws through the screw holes in the plate mount. The screws should be long enough to go through the plate mount and into half the thickness of the tabletop.
Turn the table back over so that it is standing on the legs and position as desired in the lounge room.