Doing smithing trophy starting from the Tradeskill quest Freshman Smith Trophy since my smithing skill already qualified for the Freshman version rather than the Begginer or Appentice Trophy quest.
After getting the quest from Baubile Diggs in West Freeport tent area outside the city, I created the items as listed in AakyBonz mentioned above, turned in all those to Judge Marion Teld'mare in the same camp. At the last item turned in I received the Freshman Smith Scorecard.
Turn in the Freshman Smith Scorecard to Diggs and received Beginner Smith Trophy and Freshman Smith Certificate.
Equip the Beginner Smith Trophy in primary hand, put the Freshman Smith Certificate in the forge and hit combine - the Beginner Smith Trophy evolved into the Freshman Smith Trophy.
I suspect it would be similar to other smithing trophy steps higher or lower if you don't already have any version of the smithing trophy - i.e. do the quest, get the Beginner Smith Trophy and the Certificate, then combine the Certificate to get your appropriate trophy.