Choose a base for your round table top. You could use prefabricated table bases from lumberyards or home improvement stores. For a green alternative, you may reuse any stable item, such as salvaged cable reels.
Place the table top upside down on a smooth work surface. You could lay a drop cloth underneath, for example, to prevent the floor from scratching the table top.
Place the base of the table upside down on the table top, centering its position carefully. If your table top has a pattern, adjust the position of the base to complement the pattern. For example, you could align the table base and the pattern on the table top if they are similarly shaped.
Drill pilot holes through the table base and into the table top, making sure that you don't drill past the top surface of the table top. If you buy a prefabricated table base, it may already have pre-drilled screw holes, so just align the pilot holes with the pre-drilled screw holes. At the very least, you need to drill at least four pilot holes with equal distance between them.
Drive 1 1/2-inch or 2-inch screws through the table base and into the table top to fasten the two together.