With a round tabletop, you are not limited in the type of legs you can use. You can opt for the traditional four legs, which you commonly see with square and rectangular tables. You can also use a center pedestal to hold up the tabletop. Round tables are unique because a center pedestal can be used in place of four legs.
If you are trying to decide the leg type for your round table, it is really up to personal preference. Each type offers the same stability for a round tabletop. If you want to purchase pre-made legs, then a pedestal might be your best bet for a round tabletop. A wide variety of center pedestal bases are available at home improvement stores and wood furniture shops. A center pedestal is also the more common leg base for a round tabletop. Smaller tables, such as coffee tables, are where you commonly see four legs instead of a pedestal leg.
Regardless of the leg type you choose, the installation process involves the same items. You will need a drill to make holes and bolts to secure the legs. This applies for both the center pedestal and the four legs option. If you are buying unfinished legs or a pedestal, then you will also need some stain or varnish so the legs will match the tabletop.
The round tabletop should be flipped over so it is facedown on a covered surface. You can just use cardboard for the surface. The pedestal needs to be installed directly in the center. The four legs should be evenly placed around the perimeter of the tabletop. Use the drill to make the holes in the tabletop, then attach the pedestal or legs with bolts in the holes. This secures the legs or the pedestal to the tabletop. This is important because you want your table able to handle weight. If you are installing four legs not the same height, you will need to sand the ones that are too long.