At skill level and character level 40, Blacksmiths could choose to specialize as an Armorsmith or a Weaponsmith.
Weaponsmiths could later further specialize into hammer, axe or swordsmiths. One of the poorly executed ideas from Blizzard as far as professions go, it was tied to the Mithril Order pseudo-faction and peaked in Burning Crusade which added weapon sub-specializations. The related recipes in Wrath of the Lich King became largely irrelevant and the feature was completely removed in Cataclysm for the most part.
Becoming an Artisan Armorsmith gave you access to a number of new, powerful armor recipes. Specializing in Artisan Weaponsmithing granted access to devastating weapons not normally available. Base prerequisites were character level 40 and a blacksmithing skill of Choosing to specialize as an armorsmith would have precluded you from specializing in weaponsmithing and vice versa.
Horde players would first speak with Krathok Moltenfistto start the quest chain for becoming an Armorsmith or a Weaponsmith while Alliance players would speak with Myolor Sunderfury to start the Alliance versions of the same quests. They would both direct you to the appropriate quest giver behind them.
Blacksmithing specialties could be changed at the trainers for a cost. The cost depended on the specialty you wish to drop and the character's level. Once you dropped a specialty, you could then choose a new specialty for no cost.
Each specialty could only be dropped at the trainer that originally taught it. In order to switch from a Weaponsmithing subspecialty Axesmithing for example to Armorsmithing, you would first drop the Weaponsmithing subspecialty should you have chosen onethen drop the Weaponsmithing specialty before you can learn Armorsmithing.
Once you had earned either the Armorsmithing or Weaponsmithing specialty, you did not need to complete the quest line for the other specialty if you wish to switch.
The specialty would be given at no cost. During the release of The Burning Crusadeyou were able to learn any of Wratch of lick knig armorsmithing weapon subspecializations, by talking to one of the appropriate three masters in Everlook, and asking them to teach you though you must still have completed the weaponsmithing quest, as above.
The quests, however, rewarded the same plans.