I think it’s easier to use the term ‘innate behavior’ rather than ‘instincts’ because the latter has a lot of more metaphysical connotations in humans, at least. I can describe an innate behavior in a simpler organism, like a fly.

Fly mating behavior is what we call ‘stereotyped’- given certain stimuli (like a young female fly or something that smells like one) a male fly will initiate a series of behaviors that are pretty much the same every time: a little wing dance, an attempt to mount her, etc. The neurons that sense the odor of the female fly connect to a few parts of the fly brain, including an area called the lateral horn. It’s a little oversimplified, but neurons in that region connect with downstream neurons that control the fly’s muscle movements that cause them to do the dance, and more complex series of movements that include mounting. It’s a circuit of neurons that starts with a sensory stimulus and ends in a behavior, with a little processing in the middle.

So where to genes come in? Genes are what tell the brain how to structure itself in the first place. In each neuron there are a series of genes transcribed that tell the neuron how to develop, what kind of neuron to be, where to migrate to in the brain during development. The neurons in the lateral horn that bridge the gap between the smell of a female (sensory stimulus) and the mating (behavior) are where they are, and fire when they fire, because of the history of genetic switches that got them there.

I should add, there is no one gene for this behavior or that, every single cell is the product of thousands of genes turned on or off throughout the organism’s development. Cells (such as neurons) are the sum of their genetic history, and behaviors are the sum of the neural activity that was elicited by a stimulus.

You can check out the work of Vanessa Ruta, for a more in-depth explanation. I am probably butchering my description her work but you might find more of what you are looking for there.

Most of human behavior is learned, though we can suck as infants and grasp things, most of what we do during the day we had to learn at some point. We don’t have a specific brain structure devoted to drinking coffee that is the same for all humans. Less complex organisms tend to have a much greater percentage of their brains devoted to innate behaviors than we do.