Each wafer has only one layer of transistors. They then have many layers of wiring on top. They go through semiconductor manufacturing with one layer of transistors.

For each layer of metal, they go through several steps of deposition of insulator, masking, etching, deposition of metal (often in several passes now), grinding or etching that, and then covering it all up with more insulator and grinding that layer down to produce a smooth surface for the next layer.

Once the chips are complete, 3D stacking is a packaging process. It involves grinding the backsides of the chips down until they are very thin and attaching the dies together using vias that run through the thin remaining silicon layer.

EDIT: Flash memory today has multiple stacked doped silicon layers, but it is a special process that is largely unsuitable for logic.