Strip the old finish from the table using a wood stripper in either liquid or gel form. Use cardboard or plastic to keep the old finish and stripper off the floor.
Clean the table top and neutralize the stripper using the chemical recommended by the stripper's manufacturer (usually lacquer thinner or naphtha gas) and allow the surfaces to dry for at least several hours.
Sand your table top first with medium-grade sandpaper and then with light-grade sandpaper to attain the maximum level of smoothness. Since your kitchen table may have already received a fair amount of abuse, be sure to take this chance to smooth out the table's nicks and scratches before the finishing.
Thoroughly remove dust from sanding with a damp rag and allow the table's surfaces to completely dry.
In a dust-free location, select a polyurethane finish for your table. Polyurethane finishes are more durable and water resistant than oil finishes, making them generally more suitable for kitchen tables.
Stir the container well before applying the finish evenly with a natural bristle brush, stroking along the grain of the wood.
Apply a second or third coat for best results. Allow time to dry between adding each coat and wet sand the finish between coats, lightly rubbing the surface each time until it is smooth. Do not sand after the final coat.