Museums are wonderful but funny environments. It's one thing to come across a striking painting at someone's home. You react to it or fail to react to it. You might or might not be inspired to comment on it. You don't necessarily feel there's a cultural job to be done in the presence of the painting.
At a museum, where we're told that the works included are important, some of the naturalness can go out of the experience. I don't know about you, but I've definitely had the museum meta-experience: I'm looking at the art while I'm watching myself look at the art and waiting to see how I react. I stand there wondering if I'm doing it right.
One of my favorite take-aways from art school is that I learned a standard approach for how to look at a piece of art. The first question isn't "Do I like this?" The first question is "What's going on here?" Professors would put up a slide and simply ask students to describe what they see -- everything from questions of form and color and perspective to what the people in the painting are wearing or doing. This is such a useful tool. It shuts off the part of the brain that thinks it's important to give the art a thumb's up or thumb's down, and instead engages the part of the brain that notices and catalogues and starts to propagate curiosity.
In the noticing, we learn. Sometimes we learn what we tend to notice, and sometimes we learn a little bit about what the artist might be trying to say. The noticing is essential.
After that, it might be useful to read a bit of wall text (or engage that new app!) to discover the stuff about the painting that you could never figure out by yourself -- biographical insights, historical context, things like that.
I have noticed, since learning this better way to approach a piece of art, that every time I visit the museum, I want to go back the next day. I want to slow down and look at maybe just a handful of pieces and think about them. And really look. It honors the artist, and what he or she was trying to do, when we slow down, stop watching ourselves and wondering if we're having the "right" museum experience, and really look.