Classical Music Search Tip 1: Post Your Question to a Forum
This is, perhaps, the best way to get the results you want, or at least give you a better sense of what direction you should be heading. Visit my classical music forum and drop a line. You will find that many of the users are classical music buffs that can't wait to help someone and share their knowledge. If you don't have a membership, don't worry; it's free and easy to do. Here are some great examples of what you can expect to find...
Missing Liszt Piece
Any works for solo viola?
Classical Music Search Tip 2: Search Amazon or Barnes and Noble
In most cases, the title of the classical music work and/or composer is known. The easiest thing to do is to search Amazon or Barnes and Noble. Most of the classical music albums have 30s-1min sound clips available for you to listen. If you are looking for specific recordings or variations, you'll most likely come across them using this method of search.
Classical Music Search Tip 3: Search Classical and Opera Music Used in Movies
For many beginners, this is a classic example of discovering classical music. You hear a song in your favorite movie, but you have no idea of the name of the piece or the composer. Most of the websites listed in the link above have the option to search for the music by the title of the movie. How simple! In most cases you will find the classical music for which you are looking.
Classical Music Search Tip 4: Visit Your Local Public or College Library
Another great place to look (if you don't have the option of getting on the Internet in Tip 2) is your local public or college library. At the library, you are free to listen to the entire piece of music instead of a 30 second clip. This may be more beneficial to you if you are still unsure. Also, many colleges and universities, especially those with music departments, will have a music reference section and a support staff to help you in your endeavor.
Classical Music Search Tip 5: Ask Directly
If you hear the piece on the radio station, on a website, or in a department store, call them and find out what piece it is. In 9 times out of 10, they will be able to help you. I've had many successes using this method. For instance, I really liked the music played on the San Francisco Ballet's website a few months ago. I sent them a simple e-mail and followed up with a phone call. A week later, I had the name of the piece and the album it's on.
Classical Music Search Tip 6: If All Else Fails
If all else fails, don't worry. Just keep your ears open; it's bound to cross your path again someday. On the bright side, you will surely find many great pieces of classical music you wouldn't have before had you not started searching in the first place.