As always, the most important thing to do when you are listening to the music is to listen to it. Enjoy it and pay attention to your own personal reaction to it. The following suggestions are not necessary to enjoy the music or to "get something" out of it; they are suggestions that apply if you want to learn more about music theory, practice, and history while you are listening.
While you are enjoying a classic rag, see if you can hear the syncopations. Tapping your hand or foot to the beat may help you see how many important notes are not on the beat.
Speaking of that strong beat, this was dance music. Children and other uninhibited people may want to heed the invitation in the music to move to the beat.
Can you hear the accidentals and chromaticisms in the music? Many of them involve short sections of a chromatic scale.
Can you hear the repeated sections? Can you hear a key change at the beginning of any of the sections? Because the sections are repeated and have such definite endings, rags can be a great place to practice listening for the form of a piece of music.