Turn off all electronic devices and do not turn them back on until you are far, far from the exhibit. You will live without them for a spell; in fact, you are likely under their spell. Put them in their place and try to open up to new areas of culture and history.
I have found that you need a certain arrangement of people to profit from the experience, unless you are going along (which has its charms, especially for introverts). Some people want the visit to be a socializing event, and thus will talk less about the art than about anything else. If you are an art-lover, this is annoying. Furthermore, to get deeply psychological, some combinations of folks do not work well. Let us say Person A wants to talk about the art with Person B and Person C. But Person B dominated the discussion by clinging on to Person A at the exclusion of Person C of the discussion, thus causing Person C to be ticked off at both Person A and Person B. This is not good.
Going to an exhibit with a painter or expert on art adds much to the experience. If you can do it, listen to that person and ask many questions. If you are an artist or expert, do not be afraid to comment, but not at the expense of the ideas of others with whom you attend the exhibit.
It is usually best to follow the path of the exhibit in a linear fashion, since that was intentional by the curator. However, there are obnoxious people who talk too much or too loudly or both. If so, you may need to skip ahead or lag behind. The alternative of telling off the blokes will not usually work.
Do not rush your way through the artworks. Linger and gaze on them. Look at them from various angles. Read the accompanying textual material, if their is any. Listen to the audio, if available. Ask your companions what they think and why.
When you are finished, you may want to purchase a book that accompanies the exhibit for further reference and reflection. You may even want a print of one or more of the paintings or sculptures. It is best not to immediately jump into some other immersive activity, but to let the experience settle within you.
You should consider visiting a particularly excellent show more than once. I attended “Modern Masters” at the Denver Art Museum four times, once by myself and then with various combinations of friends three other times. Each visit was unique and enjoyable. Even on the fourth visit, I discovered things I had missed the first three times.
Painting is one of culture’s greatest gifts to all of us. Even ugly and off-putting pieces may tell us something significant about culture and history. Deep and great works enlarge our understanding and please our sensorium. Let your mind dwell on these good things, as the Apostle Paul said.