~ Basics ~
In order to do anything Alchemy related, you have to go to this page:
Alchemy Page
Everyone starts off at level 1 and gaining experience requires you to create items. It takes 10 formulas of your current level to advance to the next or 40 formulas of 1 less than your current level. Anything below 1 less than your current level grants no experience.
The official Alchemy store is:
Bifrost Shop
How to use Alchemy to make stuff:

+

/

/

/ETC. + ALCHEMY LEVEL +

Basically the requirements to make anything require a formula, the ingredients, Gaia Gold, and a certain Alchemy level.
After you have all the requirements, go to the Alchemy Page mentioned above, click the
READY tab, click the COMPLETE button, and you will begin to make the item.
Every formula has a CHANCE to succeed. You can see the chance by going to your inventory and clicking the formula.
If you succeed, you will see this for a split second:
If you fail, you will see this:

You will lose the gold spent but you keep the ingredients apparently.
Where to get FORMULAS:
Aside from the Bifrost Shop, the Cash Shop is selling the formulas for all the RIGs at 1GC for each formula. To see older RIG recipes than Valefor Academy, make sure to set the show from "Featured Items" to "All Items" and the recipes will appear.
The other place to get formulas is through our old giftboxes. It seems that the gold, brown, pink, and blue ones all give recipes. In addition to those, wooden and golden trunks give out formulas as well. The Fat Cat Alert! has also been shown to give formulas.
The location of the rarest and most sought out formulas lie in the ALCHEMIST'S CASE.
Tip: There is no formula tab when trading but they DO show up in the All Items tab.
As of now, Evolving Items, some old RIG rares, and some new items are known to have formulas.
Where to get INGREDIENTS:
Ingredients range from zOMG items, Gaia equippable items, and new special GAME items.
The zOMG items come from zOMG (I recommend playing it as it is fun and good way to make gold), the Gaia equippable items come from older RIGs and are generally found only via the marketplace (but some are just gold shop items), and the new GAME items come Daily Chance, the Philosopher's Cache, Enki's Catch,and Golden Giftboxes.
NOTE: The Philosopher's Cache contains almost 90% of the alchemy components out there.
TIP: Because Dumpster Dive now gives Daily Chance items, doing it may result in ingredients!!
Leveling:
I want to first say that I am currently a
level 3 alchemist and what I have here is from other users and not from personal experience.
Leveling your alchemist level is important if you want to be able to craft the higher level formulas. Higher formulas are the more sought out items and will be very rewarding but costly at the same time because it seems that leveling will take quite a bit of gold.
Each subsequent level takes more experience. As of now it takes 10XP to get from 1 to 2 and 20XP to get from 2 to 3. It appears that each level requires 10x formulas crafted at your current level. Formulas at 1 level below your current level grants 4x LESS and therefore you need 40x of them to advance.
For example, if I'm level 3, I need to craft 10x level 3 formulas to get to level 4. If I were to craft only level 2 formulas at level 3, I'd need 40x of them. You can mix and match but experience points do not carry over levels!!
It has been brought to my attention that the higher levels you go, the less experience you get from lower leveled formulas. Someone mentioned that as a level 3 alchemist, they no longer gained experience from level 1 formulas so be vary of that. THIS HAS BEEN CONFIRMED!!
You DO get an achievement and some achievement points for each Alchemy level you gain.