Make a template for the tabletop with butcher or builders paper. If you're making a large table top, tape pieces of paper together side by side. An economical alternative is to use newspaper, but the flimsy paper is harder to work with. Draw the outline of the tabletop with a pencil and cut it out with scissors.
Lay the template down on top of a piece of ¾-inch plywood and tape it in place. At this point, you can either use the taped down template as a cutting guide or trace the pattern onto the wood.
Set the plywood on a pair of sawhorses and use a saber saw to cut out the top of the table, either following the edge of the paper template or the traced outline.
Use coarse sandpaper to smooth the cut edges of the tabletop and the imperfections in the top. If there are knotholes or other similar imperfections, apply wood filler with a putty knife, let it dry and sand it smooth. Wood putty takes at least an hour to dry depending on the thickness of the application.
Paint or tile the top and edges of the coffee table. Apply several coats of polyurethane over paint and use grout sealer on tile. Let the polyurethane dry for at least four hours. To see if it's dry, gently touch the surface. If it feels tacky, it needs to dry further.
Cut three 2 x 2 inch blocks from the remaining plywood. Turn the coffee table top over and use wood glue to attach the blocks to the bottom of the table -- two along the straight side opposite the curve and the other at the curve. Position them where you want to place the coffee table legs. Clamp the blocks in place and let the glue dry for at least two hours.
Paint or stain the coffee table legs and let dry. Paint and stain dry at different speeds, so check the manufacturers' recommended drying times. Do the same touch test as you did with the tabletop in Step 5 if you're uncertain about drying time.
Use a drill to make a pilot hole at the top of one coffee table leg. Drill a pilot hole into one of the wooden blocks attached to the tabletop. Insert a double-ended screw into the top of the leg and screw it into place. Line up the other end of the screw with the pilot hole in the block under the tabletop and screw the leg into place. Repeat with the two other legs.