Buy a glass-polishing product. Do an online search for glass polish. A number of different products will show up, like Janvil Glass Restore and Caswell Glass Polishing Kit. Though polish won't eliminate cracks and dents, it can remove some scratches, stains from hard water, and other minor surface damage.
Apply the solution provided with the kit. Your kit may come with a ready-to-use bottled solution or powdered polish that must be mixed with water. The chemicals in glass polish work by relaxing the surface of the glass so that the abrasive compound and polishing pad can more easily diminish the scratches and improve the appearance of the glass.
Vigorously hand-buff the spot where the scratch or blemish appears. Some kits come with mildly abrasive sponges or drill-bit attachments. Only use the drill attachment for deep scratches you can feel with your fingertip, up to about .004 inches deep.
Replace the glass. There's no way to eliminate cracks and chips. Replacing the glass is the only way to restore a tabletop with severe damage.
Search online for a local hardware store or website that sells small pieces of tempered glass. One Day Glass is a website that allows you to customize cut glass.
Choose the shape. Options include ordinary shapes like circles, squares, and rectangles. You can also go with an octagon, oval, or a rounded-corner square.
Pick the dimensions, thickness, tint, and edgework. The thicker the glass, the more durable it will be. However, all glass is susceptible to scratching.