Purchase a can of "Brasso" or equivalent and it should shine up like "a new penny".
For real tough "black spots" one can use EXTRA FINE steel wool and then polish with the Brasso.
It will slowly form a darker patina over several years so its not necessary to "reseal" it unless you want it to stay "looking new". But my opinion, an "old brass Stiffel lamp" really should look a little old.