Mage

Forgemage (carvemage for carvers) is an optional job for high-level smiths and carvers. They can change the element of weapons with element potions, and imbue them with extra bonuses using runes.

Becoming a mage
To become forgemage, talk to the NPC at (-5,-12). You must be level 65 or higher in the profession want to become forgemage in.

Crafting
There are two possible recipes: weapon + rune and weapon + element potion.

Element Enchant
An element enchant changes the element of a neutral weapon into another, at the cost of a reduction in base damage. The element of the potion decides the element, and the type of materia used to make it determines the damage loss. If the weapon doesn't have a neutral damage component to convert, the forging will automatically fail with "no such recipe".

Rune Enchant
A rune enchant gives the weapon additional bonuses if successful. The type of rune determines the bonus type, and the level of the rune gives the size of the bonus.

Leveling
Leveling a forgemage can to a certain degree be considered useless. If you do decide to level, the experience gained is. One important point you'll notice quickly is profession level caps. If you level up, any extra experience you might have earned is lost. So don't waste your best weapons on the first levels.

Success Rates
This is a very important section.

The base success rate starts at 5% and reaches 94% at level 100.

The base success rate listed in your profession window is just that, your base success rate. Around level 40 or so, you'll probably start suspecting the actual rate is lower. This is because it is. All bonuses on the weapon you're enchanting reduce the success rate. Note that the minimum success rate is always 5%.

The reason some reductions are too large to make sense is that the values are made for use in other parts of the game and simply applied to forgemaging as an afterthought.