Solid newel posts are best mounted from all four sides with L brackets, attached to the post and the face of the stair tread, or floor. These brackets will hold the newel steady for years to come, but present another problem, they are unsightly. The simplest solution is to wrap the base of the newel post in baseboard moulding to conceal the metal brackets.
Measure the width of the newel post faces on all four sides with a tape measure. Measure the bracket from the newel post, along the floor and up the post's face. Select a hardwood baseboard moulding in a complementary grain tall enough to cover the post portion of the bracket, and thick enough to cover the floor portion.
Cut four pieces of moulding to fit the post with 45 degree mitre cuts at each end, one right and one left. Make the mitre cuts with the moulding standing on its bottom edge, so that the pieces will wrap around the post base, framing it.
Mark the position of the bracket on the bottom and back of the moulding and use a wood chisel to shave away enough material to clear the bracket, so that the moulding will rest easily against the post and floor, concealing the bracket.
Glue and nail the moulding in place, surrounding the base of the post, with the 45 degree mitred corners meeting up to create crisp 90 degree corners. Use wood glue and a pin nail gun with 2 inch nails to fasten the moulding in place.