To make mud bricks, use soil or subsoil with 15-30% clay, and 50% or more sand, and add chopped straw or chaff. The traditional Egyptian practice was to mix Nile mud and desert sand to get the ideal consistency. Mix with water, and put the mix into your forms/molds, and leave it to dry. Usual Egyptian practice is to dry them for 3 days, and then turn them over, and dry them for another 3. The bricks can be used then, but it's better to dry them for longer - to dry longer, they're turned onto their side, for better airflow when drying. Done!

Too little clay, and the brick will be crumbly. Too much sand, and the brick will be crumbly. Too much clay, and the brick will shrink to much when drying and probably crack. If the amount of clay is fairly high, the straw can be left out - this will produce weaker bricks, but without any potential problems if insects eat the straw in the brick. The straw adds strength, makes the bricks lighter (so higher walls can be built), and helps the bricks dry faster.

There are some optional ingredients. Crushed broken pottery can be added. Dung can be added; dung can be used in addition to straw, or can be used as a substitute for straw. If you are a herder rather than a farmer, you are likely to have more dung available than straw, and you will use dung. Seeds are found in some old mud bricks - these might have found their way into the bricks via dung rather than being deliberately added.

The excrement referred to in The Satire of Trades is probably this dung. You don't want to use just any dung! You want dung with a high content of plant fibres - cow dung is ideal. Other dung would work well too, like horse and elephant dung. Dung in small hard pellets, like goat dung, will be harder to use, but will work. Dung has at least one advantage over straw: it doesn't need to be chopped, since the plant fibres have been chewed.

There is one other possible advantage of using dung: the mud brick mixture (mud, sand, straw/dung, water) is kneaded and is then ideally left overnight, or for a couple of nights, to ferment. This fermentation produces lactic acid, which results in a stronger brick. Lactobacillus bacteria which are responsible for this fermentation are found (in large numbers) in cow dung (and other dung), and the addition of dung is likely to result in faster and more uniform fermentation of the mixture.

While squeamish modern urban folks might think that this sounds very yucky, cow dung isn't nasty stuff. The smell is minimal (although cattle feedlots with huge amounts of dung can easily be pretty stinky). Some country folks (mostly children) delight in the feeling of standing in fresh cow pats and having the warm dung ooze between their toes. In many parts of the world, cow dung is used to plaster internal floors and exterior courtyards or yards (reducing dust is one useful function of this). Dried cakes of cow dung (and sheep dung) are important cooking fuels in many parts of the world. While many of today think of dung as a waste product, it is often a valuable resource in traditional societies (and in addition to the uses already mentioned, is valuable as fertiliser, and in some rural areas today is used to produce methane for use as cooking gas).

References and further reading:

Emery, V. (2009), "Mud-Brick", UCLA Encyclopedia of Egyptology 1(1). https://escholarship.org/uc/item/7v84d6rh

Morgenstein, M., & Redmount, C. (1998), "Mudbrick Typology, Sources, and Sedimentological Composition: A Case Study from Tell el-Muqdam, Egyptian Delta", Journal of the American Research Center in Egypt 35, 129-146. https://doi.org/10.2307/40000466 https://www.jstor.org/stable/40000466