Apologies for the poor quality images
It looks to me like a single colour offset litho print, using one "special" ink (ie the turquoise/blue) instead of the normal Cyan / Magenta / Yellow / Black.
Hard to say. Could be any number of processes:
- one color offset (as Digital Lightcraft mentions) likely using a spot color (Pantone)
- one color screenprint (unlikely but if it's a limited run poster, maybe)
- color laser
- low-fi one color duplicator (such as a Risograph)