In the case of Relic Weapons, the weapons begin with one damage and 999 delay (with the exception of the horn that has no stats, and the shield that has one defense) and are upgraded with Dynamis Currency and other items traded to Switchstix and eventually a specified Blank Target giving the final form. Relic Weapons can be further upgraded through the Trial of the Magians.
Alternatively, Relic Armor starts with usable stats (though how useful it is to the job that can equip it varies from piece to piece). Relic Armor can be further upgraded into Relic Armor +1 by trading the original piece with the corresponding Relic Armor -1 specific crafting materials and Dynamis Currency to the NPC Sagheera in Port Jeuno. Relic Armor and Relic Armor +1 may also be upgraded to Relic Armor +2 through the Trial of the Magians by trading a certain number of Forgotten Items to the Magian Moogle with the blue puffball. (Relic Armor requires 50 items, Relic Armor +1 requires 30.) Relic Armor +2 may be further upgraded with augments that improve merits and two-hour abilities.
It is possible to reforge your Relic Armor from its base piece obtained from Dynamis, directly to its Item Level 109 variant, and even further to its Item Level 119 (+1) variant. If you have Relic +1, +2 or +2 augmented, naturally the cost is cheaper to gain these varieties.