There are a lot of missing steps people don't really understand yet R.E. how this all amounts to something complicated like "a liver". But we think that the basic building block of it is that there are gradients of chemical concentration that some cells set up, and then other cells react to the level of the chemical and decide to different things. There's a famous analogy of the French Flag Model, where the different stripes of the French flag are imagined to emerge from how far you are from the left edge where a "morphogen" chemical is coming from, because cells detect and react to different concentrations of the chemical in different ways.

And the cells do these things because the DNA programs them to do it. Some genes produce proteins that can turn around and bind to the DNA that encodes other genes, and make those other genes produce more or fewer proteins of their own. Proteins can be made so that they bind or unbind DNA in the presence of other proteins, or particular chemicals, or which can function to turn one chemical into another. So you can have little logic circuits made out of genes that measure chemicals and turn other genes on and off. And you can have little memory circuits based on which genes have things bound to them and which ones are currently on or off, so the cells can remember what it is they decided to be. And so the cells are programmed to differentiate into progressively more specific cell types over time depending on what signals they see, with the morphogen gradients or combinations of them allowing the cells to have some idea of where they are in the body.

And the proteins are these little squishy clicky things, like long strings of magnets that will snap into certain shapes, or that can swap between a few shapes. They can be shaped so they fit really nicely against certain shapes of DNA sequence or other proteins, or so that they fit really nicely against small molecules with a piece pushing on the molecule in just the right place to make it easy for an atom to break off the end of it or whatever. And because they live in this weird tiny world where everything is constantly vibrating around and banging against everything else (because of how tiny the volumes get when you shrink the lengths to cell size), this is enough for them to find and stick to the stuff they are shaped to stick to.

Then depending on genetic variation between people, the proteins involved can e.g. have different set points for the concentrations they react to, and that can translate into the threshold between cells deciding to do one thing or another moving around in the body, and in turn translate into people having e.g. a wider or narrower region of their face decide to be a nose.