Software Serial

Having some trouble with getting serial information through the arduino using anything other than the USB serial interface. According to this tutorial, I should be able to send i/o through the digital pins.
http://arduino.cc/en/Reference/SoftwareSerialExample
However, I’ve been getting some odd results. When I plug in the external power and serial cables, the LED on pin 13 does light up; however, it continues to light up even after I unplug the serial cable, so clearly I’m not getting the result I want. Any thoughts?

How are you converting the serial signal levels to the TTL levels used by the Arduino?