"We humans are lucky - we get a lot of our neural nets pre-sized and pre-weighted and it only takes us forever to do things"
That's not how ours work. ANN if various stripes are an attempt to use a neuron based model as a computer for complex tasks. The more the explanations for the various mechanics of operation of our neural networks expand, the end point is always a case of we don't know, PHD and dragons be here. When I say "we don't understand" there generally is a much more detailed answer that I can't give :)
We are born with a brain consisting of assorted regions, divided up by the distribution of the various specialised cells. The neurons are the obvious candidates for much of the processing, and are conveniently huge in various species (such as squid) thus have also been the focus for much of the research. All your sensors, all your motor controls, active and passive, all done by the same type of cell, "wired up" differently for each purpose.
Most of the calories we consume are spent turning chemical energy into electrical standing charge for our organic computer. We share various of the same brain regions as other species, but size and density of various cells vary. We certainly do not have the biggest or best brains by any measure. Size not always better.
We grow our own brain based on the genetic patterns we have. Those neural connections continually strengthen or wither depending on how we use them, we start with many nodes but no edges. Fire a connection less often, neurons disconnect. Fire it more, strengthen the connection, make it esier to fire. You lose roughly half your neurons between birth and the age of two as you figure out how to make the brain and body mesh and control various things. Your neurons will even migrate to other regions of the brain*, based on some mechanism we don't understand. You lose more as you grow older, but you'll notice that old people are still quite clever, despite not having as many neurons as those whippersnappers. It's also why you both learn and forget a lot during your childhood, why small children will effortlessly learn new languages.
The neurons connect, interact, grow and retract in a myriad of ways that is still not understood. The rest of the cells that maintain and support the neurons also play a part in communicating between the neurons, again in ways that can be observed and modeled, but not fully understood. Even just how the eye works is a testament to evolution as an engineer, since it's a bit of your brain exposed to the world behind a few bits of skin, and some cosmetic bone with a hole for the data cable ;)
Neuroscience is fascinating. Meat computers are are darn fine things, I'm sure there will always be a place, even when the robots rise :)
* bloody immigrants form the dorsal region, they should go back where they come from, taking our jobs etc etc