IF you using the thaumatrium, you put a catalyst in the top slot of it's gui, the thaumatorium will then prompt possible results, and display needed aspects. For example, if you were to put glowstone in as the catalyst, it'll prompt nitor, and will have a white down arrow showing, clicking this will move the thaumatorium to prompt for the glowstone duplication recipe. To go back to nitor you'd simply click the white up arrow. When the thaumatorium is displaying the desired output, right click the output itself. It'll lock in that output. If for some reason you change your mind, you can right click that output again, and it'll go back to prompting.
When it's locked to an output it'll show the output on it's front, and it'll pull in essentia via tubes connected to the holes. These can be attached to warded jars or essentia reservoirs (or the Thaumic Energistics supplier thing or alembrics, both of which can be directly attached). Once the thaumatorum has all the needed essentia, it'll consume a catalyst and spit out the bigger hole the output. If there an inventory in front of this hole it'll be placed in that instead. This is all you really need to know for manual use.
If you automating one, you can attach menomic matrices to the holes in place of tubing or other essentia input, this will cause the thaumatorium to gain 2 extra slots for recipes.
EDIT: As for essentia sorting, due to intracies with the piping system, golems are far and away the easiest method for handling multiple essentia types (assuming no thaumic energstics which obsoletes both golems and tubing in it's ease of use.)
If you REALLY want to use essentia tubes, you are going to need essentia buffers and either filtered essentia tubes or labeled jars a plenty. I've not got any screenshots or further help on this though, as I prefer golems by far.