Any repair NPC can show you this book, by selecting their "Learn about repairing" option when you speak with them.
As all know, the regular use of weapons and tools exacts its tool. Wear and tear accumulate, and, if ignored, will render the best of equipment near useless. The same follows for armor and accessories, as over the course of time they are damaged by the blows of enemies, or worn dull by heavy employ. The degradation of an item's condition can only serve to lessen its effectiveness. To prevent this and any resulting woes, regular repairs are an absolute necessity.
There are two schools of thought pertaining to the repair of items. The first of these entails entrusting one's possessions to a shop which specializes in making repairs. The services of such establishments are available at any time, but tend toward high prices. Moreover, the repairs will not restore an item's condition to mint.
The second option is to have repairs made by a fellow adventurer to adheres to the Discipline of the Hand. First and foremost, you have to decide upon the item that you wish to have mended. Next, the payment that you propose to make in return for the requested repairs must be set - be it in gil or an item. Once the repair and payment settings have been made, you need do no more than wait for a crafter trained in the proper skill to approach you. Should they not, reconsider your payment. Ofttimes, the unanswered offer, offers too little.
Conducting one's own repairs can be extremely satisfying, and well within the possibility for any crafter. The process is equally as simple as employing the services of another, if not more so. Decide upon the item you wish to mend. Then, you need only make sure that you have the proper materials required to make the repairs in question.
The ambitious crafter should be forewarned, however, that both profession and skill will limit the range of what he or she may fix.
Further, all Disciples of the Hand, save the culinarians, may undertake the repairs of their fellow adventurers. Those seeking to do so must be ever watchful for opportunities, perusing bazaars whenever possible. Should you come across someone in need of repairs that fall within your ability, see next that you find the proposed reward acceptable. Then, offering your services is as simple as accessing the item by way of the client's bazaar. Mind, you must be in possession of the required materials before any repairs may be begun.