Although it's fairly popular, a lot of people can't stand classical music. Why? Well, some say it's too slow, some say it's too fast, others think it's too gleeful, some guys simply want distortion, and some others want autotune. Yeah, that's where music is going. (Unfortunately).
So, how can you appreciate this music? Well, first of all, you need to develop a musical ear. You know, tell the difference between instruments, find the beat, all of that. I you're good at dancing, it'll be easy. Same goes for playing an instrument. Once you get it, you can enjoy any kind of music, but it doesn't really stop there.
You can make a challenge for yourself and try to remember more composers than Mozart and Beethoven. There's a huge bunch of good music waiting to be listened to, like Brahms, Tchaikovsky, Johann Sebastian Bach, Frederic Chopin, Vivaldi, and many more. You know, there's a variety.
If you like solos, go for music like Vivaldi or Chopin, who make great violin and piano solos (in their respective order). If you like sonatas, hear a few of Beethoven's. You know, find the music for you. After a while, you'll love it, really.
Like I said, don't just go for popular music. Listen to Paganini (who is actually fairly popular, just not as much as Mozart), view the concerts of people like David Garret, you can even listen to Apocalyptica, and Yngwie. In the end, classical music's an acquired taste, but that raised IQ can't hurt, right?