The easiest first step is to just go out a purchase a classical CD that contains a compilation of several different composers. If you really want to get a good feel for the wide variety, then you may want to purchase several different compilations.
Now just let the music play in the background during the day whilst you do other tasks. In most cases it won't be incredibly distracting, so you'll be able to listen o it at work or at home.
After you've been listening to it for a couple of days, start paying attention to specific composers that you enjoy. Take note of their names and begin seeking out additional classical music composed by them.
Once you've identified a particular style you like, start attending concerts that fit your tastes. This will greatly increase and enhance your appreciation for the music. You'll get far more information about the premise and meaning of the music as the composer often will explain this between sets.