(1/25th of the line at Musée d'Orsay)
(Venus de Milo at the Louvre)
1) Get there either right when the museum opens or about an hour or two before it closes (depending on how long you want to spend inside the museum). If you're an early riser, the first option would be good for you, while I prefer to sleep late and live on the wild side, taking my chances on the outer edge of gaining entrance. Anything between these two strategies and you will be waiting outside literally for hours.
2) Bring a snack. I know it's not allowed, but, like I said, wild side. You can always go off to the side or into the bathroom and nibble on a granola bar. I'm hypoglycemic so if I'm going to be anywhere for two hours I need to bring a sugar boost with me, lest my companions bear the brunt of my truly astonishing bad hunger moods. Also, obviously, wear good walking shoes and don't feel guilty about sitting down and taking a break once in awhile. Sometimes it's fun to watch other people experiencing the art while you recharge.
(Mona Lisa at left; the rest of the world at right, at the Louvre)
4) Know where to go. If you're hitting up an institution like the Louvre, and you want to see a specific piece, look it up before you go. There are four floors and hundreds of rooms, and it's easy to get lost in its various wings. For me, it took three visits to the Louvre and detailed directions to finally find my favorite piece of art, Antonio Canova's Psyche Revived by Cupid's Kiss. But once I did, the thing was so tucked away in a sunlit corner, with no one else around it, that I felt like it was my own.
5) Or, feel free to wander, and don't be afraid to walk away. If you're at the Louvre or Centre Pompidou, you will probably not see everything the museum has to offer in one day (definitely not at the Louvre). The amount of art in one museum can be astounding, overwhelming. A modern art museum like Pompidou is designed to appeal to many tastes; not everything is for everybody. Have an opinion. If something doesn't strike your heart, don't be afraid to move on to that piece across the room that is pulling you in. Spend as much time as you like absorbing the art that moves you inside. When you go home, you won't remember what you didn't like; you will only remember the pieces that made you feel like there was nothing else in the room but you and the art.
Now go forth and absorb! Here's a list to all the free museums in Paris.