discounts

That is so broad it is impossible to answer. Which museums, which countries, your age, occupation, time of year, etc. In general discounts in Europe are not as easily obtained as in the US. Most guidebooks will some information on this subject. Try doing some of your own homework.

Read the webpage for each museum to see what discounts are available.

Depending on the cultural site or program, you may be eligible for student, senior, or family discounts. Many museums offer free days or free hours. Otherwise, a city pass or museum pass may make sense if available. As previously mentioned, check the websites for the places you’re planning on visiting. Generally (and beyond savings for museums & sites), there are many ways to cut costs on your trip…review Rick’s suggestions: http://www.ricksteves.com/plan/tips/thrifty50.htm

Apart from those already mentioned--student, teacher, and senior discounts in SOME places--there's not much of a chance, in my experience. I'd also proceed with caution in booking so-called 'discount' tickets: while it never hurts to ask, be sure you're asking the official site or museum itself, or you can be burned by getting cheap tickets to sites/museums that don't allow you full access. If, ultimately, you travel all the way to Europe but don't see what you really traveled to see, saving a few bucks isn't really a bargain.