In practice it's very systematic for small networks. You perform a search over a range of values until you find what works. We know the optimisation gets harder the deeper a network is so you probably won't go over 3 hidden layers on tabular data (although if you really care about performance on tabular data you would use something that wasn't a neural network).

But yes, fundamentally, it's arbitrary. For each dataset a different architecture might work better, and no one has a good strategy for picking it.