This is where it starts. Empty bottles get loaded into the iron chest to be put into a Dynamism Tablet set to right-click them on an Everfull Urn, thus filling them with water. An Empty Golem then takes them to the first set of Brewing Stands, to be pictured shortly. (In my modpack, this is the ONLY way I could find to fill bottles with water. And I tried a lot of different things before finding this.)
A small melon and netherwart farm; the netherwart is harvested with RoC fans and the melons with pistons; they are blown (via fans) down to the end and into a Hungry Chest. The piston is to push the melons in.
The water bottles get sent to the first pair of brewing stands to be made into awkward potions; those are sent to the second pair. Meanwhile, Netherrack is sent from a Boring Machine in the Nether to a Rock Melter (The machine in the bottom left) to be turned into lava, which gets sent to a Drying Bed to be turned into gold nuggets. Those get sent to an autocrafer to get combined with the melons. The resulting Glistering Melons get sent to the second pair of brewing stands to be turned into Healing Potions. They then get sent to the third pair of brewing stands to be enhanced with Glowstone.
The aforementioned autocrafter; I use the RoC one because it can hold multiple recipes at once.
Netherrack from the Nether bore also gets sent to the Infernal Furnace to be smelted into Nether Bricks, which get sent to the autocrafter to be turned into Nether Brick blocks. These get sent back to the furnace to be smelted again into Nether Stone from Railcraft.
Now, I know the essentia tubes look wildly complex, but bear with me. Remember the Healing Potions? They get melted down in the furnace on the left into Sano and Praecantatio, as well as Aqua as a byproduct which gets sent to a Void Jar. The Sano is one of the ingredients for the soap; the Praecantatio is needed to make the magic tallow required. The left furnace also processes Ender Pearls (from an Enderman farm) into Alienis (another soap ingredient), Iter (gets centrifuged to make a bit of extra Ordo), and Praecantatio (to supplement the potions). The furnace on the right smelts down the Nether Blocks into Ignis (for the Furnace), Terra (voided), and, most importantly, Ordo, which is needed for the soap. The setup with the nether stone was actually added retroactively, and the factory will technically work without it, but just be aware that Ordo will be the bottleneck as the centrifuges simply do not make enough Ordo from the Iter. The right furnace also smelts down paper (made with some Sugar Cane diverted from the Ethanol factory); normally it would only make Cognitio, but because RoC adds a recipe for paper that requires a Water Bucket, it also makes Metallum and Aqua. Yes, I know I could use the Metallum to make free iron, but I consider that an exploit, so they're both just voided.
The "giant Alchemical Construct" (because admit it, it does look like a giant one of those) from the back. The void jar at the Sano output is to provide a buffer and take care of any excess. I'm okay with wasting essentia because I have copious amounts of all of the ingredients.
The giant Alchemical Construct from another angle; you can sort of see the centrifuges. Basically, Iter gets turned into Terra (byproduct) and Motus, and then the Motus is turned into Aer (byproduct) and Ordo. The Transvector Interface in the back is linked to the Thaumatorium and is the input for Rotten Flesh to be turned into tallow. I try not to think too hard about how I'm essentially cleaning my body and mind with the flesh of undead humans.
The only thing that is NOT automated in this is fuel for the Alchemical Furnaces; for that I'll probably cheap out and copy Dire's method of automating Alumentum.