It can be found as loot from chests within Dwarven mineshafts. It can also be obtained by completing mini-quests for Durin's Folk. You can also get them from killing npc's, from Mystery Webs in the Mirkwood forest, or from ruins.
It can be combined with a piece of mithril armour and some mithril mail in an anvil to obtain the True modifier. This modifier provides a level of protection against polearms: any melee weapon with melee reach greater than or equal to 130%. It is exclusive to mithril armour.
Books of True-silver are among the few items that can be stored in bookshelves.