Cut a circle of 1-inch plywood with a jigsaw. The circle's diameter should be three-quarters that of the table top, and will form the pedestal's base.
Place a threaded 3-inch metal pipe flange in the center of the pedestal base. Mark the locations of the screw holes with a pencil.
Drill a 1/16 pilot hole at each pencil mark.
Sand the entire plywood surface with 120-grit sandpaper to remove any imperfections left by the saw or drill.
Screw the flange to the pedestal base with 1-inch screws. The thickness of the flange will prevent the screws from poking out of the plywood's other side.
Place a second flange in the center of the table top's underside and mark the screw holes.
Drill pilot holes at the pencil marks, being careful not to go all the way through the table top.
Screw the second flange to the underside of the table top, using screws that match the table top's thickness. Once again, the flange's thickness will prevent them from penetrating the surface of the table. Set the table top aside for now.
Screw a 30-inch long, 3-inch diameter double-threaded pipe into the flange attached to the pedestal base. Use a pipe wrench to ensure a tight connection.
Scour the pipe and flange attached to the pedestal base with steel wool to roughen the surface.
Wrap the upper threads of the pipe in masking tape to protect them.
Brush a coat of primer onto the entire pedestal. Allow it to dry, then paint the pedestal as desired to match your decor.
Remove the masking tape and screw the table top onto the other end of the pipe.