Very few art forms offer something as big as an orchestra—one hundred people playing music that can last over half an hour.
To start with, try to identify some of the different things you hear.
The term "classical music" is a catchall for everything from solo piano works to Gregorian chant to contemporary instrumental sextets.
To help orientate yourself, start with some of the traditional smaller ensembles where three or four musicians play together.
Classical vocal music is either loved or really hated.
The piano is a classical instrument, and the keyboard will give you a variety from all over the world, from Bach's Goldberg Variations to Beethoven's 32 sonatas to Frederic Rzewski's contemporary variations on "The People United Will Never be Defeated." Listen to Chopin's piano works (mazurkas and waltzes and nocturnes) and his set of 24 preludes.
Solo works on other instruments include Paganini's 24 caprices and Ysaye's six sonatas for violin, Philip Glass's "Songs and Poems", or Tania Leon's "Four Pieces" for cello.
Following a gifted artist might be a better way to get into the field than singling out performances of masterpieces.
Particular artists whose concerts are almost always memorable are pianists Daniil Trifonov and Yuja Wang, violinists Hilary Hahn, Leila Josefowicz, Jennifer Koh, and the singer Julia Bullock.
Classical music makes a particular kind of musical statement longer than other forms and in a complex manner. It cannot be understood quickly or conveyed in any other form.
You have to think about what it is or isn't, listen to the distinct sounds it offers, recognize earlier themes, weigh the pauses and the crescendos, think about what you do get and making it your own.