I have observed people in museums approach art in many different ways. My own approach, or style, is to scan a gallery, and then to engage with particular works of art that speak to me. I allow the art to choose me, rather than the other way around. I walk up to them and just visually soak them in before moving on.  If I read the label on the wall next to the art, I only do so after I have spent time with the piece. 

Some museum visitors prefer to join a docent tour, rent an audio guide, and absorb the artist's whole bio. Perhaps due to the pitfalls of technology, however, many people seem to have decreased attention spans and/or time being present and undistracted in a museum setting.

Truthfully speaking, many visitors can be simply intimidated by art because they feel they don't understand it. Michael Findlay, in his new book entitled, Seeing Slowly - Looking at Modern Art,  the author makes the case that if they would just look at it for what it is, they would appreciate more than if they had known the whole artist's life story. The author argues that background knowledge is not only unnecessary but even hurtful, to truly appreciating works of art.

I don't think there is one right or wrong way to look at art and appreciate it, so long as we engage with what catches our eye and fascinates our imagination, aside from simply snapping a selfie with a masterpiece and moving on.