Sand off the finish on the wood. The dining room table will need to have its clear coat or varnish removed. Use a medium grade sandpaper and go with the grain of the wood -- not against it. If you go against the grain, you will end up scratching the piece. Work in short, even strokes and continue until the entire piece is smooth to the touch and no trace of the clear coat remains.
Wipe off the table. Use a very soft and damp cloth, such as a chamois, to remove any remaining sawdust and clear coat residue from the table. If necessary, use a shop vac to remove excess dust. Allow the table to dry completely.
Apply the first coat of darker mahogany stain. Use a paint brush and apply a very thin coat of stain. Go with the grain of the wood, not against it. Do not overapply the stain, as this can lead to dark spots and the finish will look sloppy. Give this first coat at least four hours to dry.
Sand the table again. This time, use a fine grade sandpaper and just lightly go over the entire table. You need to do this to rough up the finish so that the second coat of stain will adhere properly. Remove all dust from the table when you are finished sanding.
Apply additional coats of wood stain. Keep applying the stain until it reaches the desired depth of color. Allow each coat to dry and sand the table before the next coat.
Cover the table with a clear coat of varnish. Lightly sand the table again and then apply varnish to protect the finish of the wood. Work slowly and apply at least two very light coats over the wood.