This Thinfilm company claims to be able print basic displays already, and hints that the process involves 5 layers of material. I'm guessing that there are two outer conductive layers, of longitudinal and lateral electrode arrays respectively. Two of the inner layers would form the P-N junction of an OLED.

Not sure what that fifth layer would be, though. It could be something as mundane as a non-stretchable structural support. Or, it could be that there is more to OLEDs than the Wikipedia article lets on.

https://en.wikipedia.org/wiki/OLED#Polymer_light-emitting_di...

As for how this would be printed, that is probably just a matter of coaxing the required layer-chemicals into a suspension that has the right consistency for their own printers. I recall an article a while ago, about some pharmaceutical researchers teaming up with HP to develop chemical print heads that spit out protein solutions, and then spit drugs onto them, in order to rapidly test millions of different concentrations. These people might even be using that same printer.