Ok, I'm gonna explain this in steps for the noobs who've posted on this page.
Step One: Go to Dynamis-Bastok, get Relic Axe to drop. Win lot.
Step Two: Go on an insane number of Dynamis runs and obtain 3 Lungo-Nago Jadeshell ancient currency pieces. Obtain 1 Angel Skin, 1 Chronos Tooth, 1 Feather Collar+1. Trade currency and items to Switchstix in Castle Zvahl Baileys. Congratulations! You now own a Leonine Axe.
Step Three: Go on an insane number of Dynamis Runs and obtain more currency, etc etc. Trade Leonine Axe, currency and 1 Tabar, 1 Darksteel Tabar, 1 Tabarzarin to Switchstix. Wait 1 week earth time and return. Congratulations! You now own a a Dynamis Axe.
Step Four: Go on Dynamis-Beaucedine runs until you obtain an Attestation of Bravery. Switchstix transforms your Dynamis Axe into an Ogre Killer.
Step Five: Obtain Runaeic Fragment, run around Vana'diel completing cutscenes. Yada yada, you now own a Guttler.
ALL stages of relic weapons are rare/ex. You cannot wield two. If you toss away your relic weapon at any time, which you'd have to be insane to do since you will have spent months and millions (literally) to obtain each stage you can start over.