Apply a thick coat of chemical stripping solution to the oak table with a natural-bristle brush, working on the top of the table first. Leave the solution on as long as required by the chemical's manufacturer to allow the solution time to loosen and dissolve the old finish.
Scrape away loosened finish on the table top with a flat-blade scraper. Strip the table in small sections. A three-foot area is plenty on the flat surface of a table.
Turn the table upside down and place the top surface on a soft old blanket. Strip one leg, or part of one, at a time. Use curved-edge scrapers to remove dissolved finish from rounded legs.
Brush away stubborn wood finish in table leg creases with a stiff narrow brush. Wipe residual wood finish from the surface of the wood with a rag, dampened with stripper solution.
Sand the entire wood surface with 100-grit sandpaper before applying the new finish. Use a foam sanding pad to sand round table leg contours.
Create a dust-free area for staining and finishing. Vacuum, and use a tack cloth on the table and on surrounding walls to remove any dust that may mar the finish of your table.
Smooth on wood stain with a stain applicator pad, leaving it on for a few minutes before wiping it off completely with absorbent rags. The longer you leave the stain on, the more intense the resulting color will be. If you want only the natural look of the oak to show through, skip this step.
Sand the surface of the oak after the stain dries with 220-grit sandpaper. This is a microgrit, and it will not sand off new stain, but it will smooth the wood if the stain raised the grain. Rub your fingers over the table to find rough areas.
Apply a thin coat of wood finish with a paintbrush, according to the manufacturer's instructions. Standard oak finishes include varnish, shellac and polyurethane.
Use multiple thin applications of wood finish, sanding in between with a very fine 400-grit sandpaper to remove any bits of dust.