First and foremost, figure out which museums you'd like to visit while in Paris and make a list. I recommend that you don't plan on visiting each place for somewhere between two and four hours because it can be exhausting and really, it should always be fun. You are on vacation after all. If it looks like you'll be going to a lot of museums you should look into purchasing a Museum Pass. There are options for 2 day, 4 day, or 6 day passes, which must be used consecutively but allows an unlimited amount of visits to over 60 museums and monuments.
If you decide not to buy a museum pass, I highly recommend that you purchase all your tickets in advance online. They will need to be printed out and some hotels can be a bit persnickety about this so double check with your concierge on what their "printing" policy is. There are also plenty of internet cafes which allow for cheap internet access and printing.
If you are a teacher remember to bring identification because many museums offer a discount. If you are a european student age 25 or under, you enter almost all museums and monuments for free, so make sure to bring your student visa with you.
I definitely think that having some knowledge of what each museum has to offer and what you want to see prior to visiting is a good idea. Free museum information maps are offered at the entrance of each museum but these are often very limited so you may want to purchase a museum guide book. These can also be helpful because the majority of museums in France only have informational placards in french, so if you'd like to read more about individual paintings and don't speak the native tongue, a museum guide can help you with that.
For the Louvre and Versailles (which I both recommend) plan almost an entire day. The Louvre is a gigantic labyrinth and is not only filled to the brim with masterpieces, but is also a decent hike just getting around. So make sure you bring comfortable walking shoes and a light bag (the coat/bag check fills up quickly). Versailles, on the other hand, is a train ride outside of Paris. The Palace is huge and worth a walk through, and the grounds that it sits on are one of the most beautiful places I've ever been. Definitely make your way to Marie Antoinette's Hamlet which is so quaint and adorable it barely seems real (and in fact, it isn't really real). It's definitely a smart idea to go when the weather is better because a large part of the Versailles experience is walking through the grounds which are a large beautiful garden that may as well be a park it's so grand.
Other recommendations are the Musee d'Orsay and the Musee Rodin. Musee Marmottan is a bit off the beaten path but is a beautiful and small collection of impressionists (a lot of which is Monet) that's easy to walk through and not overwhelming. There's a Picasso museum (which is currently closed for renovation) and numerous other incredible establishments with a revolving door of breathtaking exhibits. Check it out before you leave or walk through the Metro to get some last minute ideas (they often advertise the larger exhibits in the metro tunnels). There are plenty exhibits currently going on (like the Alexander the Great and Forbidden city exhibits at the Louvre, the Pompei exhibit at the Musee Malliol, and the Gertrude Stein exhibit at the Grand Palais to name a few), and will have plenty more museum advice to share with you as I go!
Remember to stay hydrated, eat before you go, and try not to overdo it. It's amazing how exhausting looking at beauty can be, but that just shows how much it stimulates the mind.