How do I work out how many layers of carbon a part needs?

It depends on the loads, the span and the shape, so there is no single number that fits every part. As a starting point, finished thickness is roughly the number of plies multiplied by the cured thickness of one ply, and that ply thickness follows the fabric weight, so a 200gsm woven ply ends up around a quarter of a millimetre once cured. For a cosmetic skin over a mould or core, one or two plies is often plenty. For anything that carries real load, the layer count and the fibre orientation both need to suit the forces involved, and it is worth running a proper laminate calculation or getting engineering input rather than guessing. Send over the details of the part and the loads it will see and we can point you in the right direction.