[I'm going a lot by vague memory from reading the old alchemy guide back when it still existed, a little bit of experimenting, and by what I've been told here, so I may be wrong about some things. Please fix as appropriate. --Ashen]
Alchemy is the process of creating tinctures from various components to produce possibly useful compounds. Primary Tinctures are created in an Assimilation Bath using Grain Spirits and various materials such as herbs, ores, and other items. They are combined into Compound Tinctures using an Alchemist's Bench, which is powered by Petroleum.
Each Primary Tincture (and each Compound Tincture while it is still in the Alchemist's Bench) has two numbers associated with it. The lower number always appears to the left and the higher number to the right of the tincture's name. These numbers determine whether or not tinctures will combine in the bench: in order for two tinctures to combine, the sum of either numbers from one tincture and either number from the other tincture must be -1, 0, or 1. The resulting combined tincture will drop these two numbers and keep the other pair, again with the lower number on the left and higher number on the right.
-17 Af -13 -15 Nu 13
Will combine to:
-17 AfNu -15
...because -13 and 13 add to 0. However, a Primary Tincture will not combine with itself directly. Adding two -20 Ki 20 tinctures will not result in -20 KiKi 20, but instead will leave two uncombined Ki tinctures in the batch, requiring one or more other tinctures to react with them or Reducing Agent sprinkled from the top to remove one of them. A combination like KiKi can be accomplished by using other tinctures in between and Reducing Agent injected from the bottom to remove a random part of the Compound Tincture, which may leave KiKi remaining. (Note: it does not work to, say, add Af, Rv, reduce to remove Rv, and add another Af. You would think they would join to AfAf but instead it reverts to two unjoined Af tinctures with the original Af numbers. You'd have to have the two Af tinctures joined by Rv before reducing the Rv out.)
When combining two Primary Tinctures, it appears that they always appear in alphabetical order in the combination (e.g., it does not appear that NuAf will ever result from the above; not sure this is true, but NuAf can be accomplished indirectly). This is not the case when additional Primary Tinctures are added: for example, adding -14 Hu 15 to the above -17 AfNu -15 will not (I think) result in AfHuNu, but instead (at least) AfNuHu. (Not certain if HuAfNu can ever result, but it seems probably it follows similar alphabetical ordering rules comparing the whole tincture name AfNu vs. Hu rather than the individual components).
Compound Tinctures may have uses that must be discovered via Scrying, but most do not. Further, order in the final compound matters (AfNu is not the same compound as NuAf). A tincture must be removed (filtered out) from the Alchemist's Bench to be scryed, after which it loses its numbers and cannot be returned to the bench. To remove a tincture from the bench, all of the individual tinctures must have been successfully combined into one, which may take some time.
As each Primary Tincture is added, they appear in a stack in the Bench window and combine over time. Stirring the batch may allow things to progress if reactions that should happen are not proceeding. WARNING: if there are 7 uncombined tinctures stacked up in the bench, adding an 8th will cause the bench to explode. You must wait for them to combine or use Reducing Agent to remove unwanted tinctures.
In summary, creating a specific Compound Tincture requires adding Primary Tinctures with compatible numbers that allow them to combine, probably using additional Primary Tinctures to adjust the Compound Tincture's numbers and allow it to combine all those Primaries that are desired in the final Compound and Reducing Agent to remove these extra tinctures.