Fragments are obtained by using the Salvaging skill. Only Armor and weapons (not Accessories) of uncommon (green) or higher rarity may be used in this process. When you salvage an item you are given a choice of what bonus you want the product to be based on, this bonus MUST be on the item you are salvaging. If there is only one bonus on an item, use of the skill on that item will automatically extract that bonus.
A list of fragments is found on the Talisman Making page.