Don't try and go around a whole museum in one day. Sensory overload will kick in, and you'll end up enjoying none of it.
First buy a guidebook. Then - over a coffee elsewhere - decide on one room / exhibition / single exhibit to visit. Go straight to that area / piece, enjoy it, and leave.
Repeat this another day, or even a few hours later, to see other pieces.
If you live in major city like NYC or Chicago, become a member of your favorite museum. Then when you go, watch the tourists - especially the kids. Some people have pensive reactions to art, other are comical. Just relax and enjoy. Psych yourself up for your next visit by watching "The Thomas Crown Affair" (the re-make).
If you really love the museum your kids will love it too.
Show them your favourite exhibit and tell them why you like it.
Don't lecture AT ALL - let them explore and ask the questions.