To ask how does art acquire value is really no different than asking how art (or anything at all) acquires meaning, as both concepts are significantly more hollow than any of us are commonly willing to admit into consideration.
Art itself is the reflexive recombination of (existing, pre-existing) idioms, concepts, images and narrative (cultural) threads. It represents a hyper-inflating referential space within which all “new” artefacts or cultural presences are really nothing more than the recursive introspection of the globally-distributed communications system.
The popularity and putative value of any artefact is a function of the extent to which that image or object is itself replicated across the broader (i.e. gestalt) cultural and economic context and system – as a matter of perception or material presence. Every postcard, t-shirt, web image, article, even – every memory and thought of a specific image increases its distributed and diffuse “mass-density” across the entire system. Things like this image are no different to ideologies, traditions, schools of thought or technologies – they are all components of a single, unified and endlessly-extensible, autonomously self-propagating (cultural) information system.