Enchanting will allow a player to pick an unfavorable property on a Rare or Legendary item and then re-roll to potentially improve it. The post notes that "not all properties can be re-rolled," but most can, and players will be able to re-roll those as many times as they like after paying a material cost.
Transmogrification will leave properties as they are and instead serve as a way to change just the appearance of armor and weapons. The Battle.net post states that "all items with a visual appearance" are planned for compatibility with the Transmogrification service, so long as the desired appearance has been unlocked. Keep in mind that item appearances unlocked in Normal mode will be separate from what you gather in Hardcore mode.
Step-by-step procedures for using either option are written in full in the Battle.net post detailing the character, but the gist of it is that you'll need to visit her cart to have either service performed. You can also check out concept art of how her cart will visually progress as she levels up.