I will vouch for newflasker
on the comment about the research that is mentioned (actually the WHOLE book is all about the different ways to grow Orchids from alternate means as well as Seeding).
I recently borrowed the book from the Orchid Society I belong to...and though my education in the biology aspect is VERY limited.
They DO mention a few interesting ways, though some are quite complex and need very specific growing Media and Materials.
If you have a Phal that is finished flowering, you can actually propagate MORE from the clippings made from the orchid's inflorescence.
Same goes with orchid leaves; certain parts and types of leaves can be used to culture and propagate "clones"...but as I said these methods can be very difficult to do!
Gonna take me a "little" while to get through the book, but even if I understand a 1/4 of everything in it...I will still have a better understanding as to HOW orchids can be Propagated!