Here is the developers' brief blurb on Alchemy from when it was first added in Feb, 2019:
https://gtm.steamproxy.vip/games/371970/announcements/detail/1753492327004925920 You can view some details on your current Alchemy skill by mousing-over the skill name in-game.

Prior to finding an Alembic (see below), you can still work towards your Alchemy:
-Saving potions (and empty bottles) for once you do have an Alembic.
-Filling empty bottles from faucets and fountains
-Drinking any potion type for the first time (even the bad ones) will:
--Level up Alchemy by 1 point
--Add it to your list of known Base/Secondary ingredients if applicable

In order to craft using Alchemy, you must find or buy a new item called an Alembic.
You can use an Alembic to "Experiment" or "Brew". It seems like you can cram anything together with Experiment to see what the result is, and Brew will only allow you to craft known potions.

Potions that do not get added to the Base or Secondary lists upon drinking, and trying to Experiment/Brew with them will always(?) result in Sickness:
Extra Healing
FireStorm
Healing
IceStorm
Levitation
Paralysis
Strength
ThunderStorm

Base ingredients (alphabetical):
Acid
Booze
Fruit Juice
Invisibility
Polymorph
Water

Secondary ingredients (alphabetical):
Blindness
Confusion
Cure Ailment
Polymorph
Restore Magic
Sickness
Speed
Water

Global Recipes (some exceptions noted below):
Water + X or X + Water = chance to duplicate potion, or lose both, increases with skill.
Polymorph + X or X + Polymorph = random potion
Using a potion that is not a Base or Secondary ingredient = Sickness
Using Acid in an invalid recipe = explosion (not 100% confirmed)

Recipes (alphabetical by base):
Acid + Blindness = IceStorm
Acid + Confusion = Fruit Juice
Acid + Cure Ailment = FireStorm
Acid + Restore Magic = IceStorm
Acid + Sickness = FireStorm
Acid + Speed = ThunderStorm
Acid + Water = explosion that burns you, breaks your alembic, and gives you an empty bottle.
Booze + Blindness = Strength
Booze + Confuse = Acid
Booze + Cure Ailment = Speed
Booze + Restore Magic = Blindness
Booze + Sickness = Confusion
Booze + Speed = Paralysis
Fruit Juice + Blindness = Cure Ailment
Fruit Juice + Confuse = Confuse (will be changing to Booze according to dev)
Fruit Juice + Cure Ailment = Restore Magic
Fruit Juice + Restore Magic = Healing
Fruit Juice + Sickness = Booze
Fruit Juice + Speed = Invisibility
Invisibility + Blind = Polymorph
Invisibility + Confuse = Paralysis
Invisibility + Cure Ailment = Levitation (reported as Confusion by one user)
Invisibility + Restore Magic = Extra Healing
Invisibility + Sickness = Blindness
Invisibility + Speed = Restore Magic

Recipes (alphabetical by result):
Acid = Booze + Confuse
Blindness = Booze + Restore Magic
= Invisibility + Sickness
Booze = Fruit Juice + Sickness
Confusion = Booze + Sickness
= Fruit Juice + Confuse
Cure Ailment =Fruit Juice + Blindness
Extra Healing = Invisibility + Restore Magic
FireStorm = Acid + Cure Ailment
= Acid + Sickness
Fruit Juice = Acid + Confusion
Healing = Fruit Juice + Restore Magic
IceStorm = Acid + Blindness
= Acid + Restore Magic
Invisibility = Fruit Juice + Speed
Levitation = Invisibility + Cure Ailment
Paralysis = Booze + Speed
= Invisibility + Confuse
Polymorph = Invisibility + Blind
Restore Magic = Fruit Juice + Cure Ailment
= Invisibility + Speed
Speed = Booze + Cure Ailment
Strength = Booze + Blindness
ThunderStorm = Acid + Speed

If you've discovered some other recipes (or corrections!), comment below to help with the guide. Thanks!