Vin/Vout ~ # of primary turns/# of secondary turns.
For an existing transformer, if you can
get a peek at the wire size used in winding, and
measure the winding resistance, and
measure the volume of the winding,
you could, in principle, figure out how many turns there are.
Do this with each winding and then use the formula above.
The number of turns in the primary is determined by the desired flux density in the core. Done by hand, transformer design is not all that easy. It's all non-linear.