I have had this trusty orchid for many years and it has given me many lovely sprays of flowers but now it has given me a baby orchid! I have propagated from stem plants but not sure how to deal with this.
to propagate orchids you have 2 options
1st method is the Stem Cutting method which you mentioned in the question.
2nd method is the Keiki Cutting method. (the best way in my opinion)
keep the keiki with its mother for now until gets at least 2-3 leaves and at least 1 inch long roots
caution only separate the plants when your keiki is ready there is no need to rush as @rob suggested
1 ) water the mother plant the day before you choose to separate the two to give the keiki a better chance of survival.
2) then cut the baby orchid below the roots so that it can sustain itself with it's own roots.
3) pot your new orchid in a suitable growing medium just like the mother has.
:) free orchid
keiki = baby in Hawaiian