What precautions I can take against burning my Arduino? What things I should be aware of when playing with an Arduino.

I read about people burning their Arduinos when connecting things wrongly.

I do not have a lot of electronics knowledge beyond a freshman physics course. I bought an Arduino because I am interested in the software part. 
My plan so far was to connect 'stuff' in ways that make sense to me and then experiment with software. Yet, I am a afraid that this approach would damage my board pretty quickly. 