LED's are polarised. They need to be connected the right way round to work. Plugging one into GND & pin 13 is not a good idea on an arduino made in the last 5 years (including the Uno). There is no current limiting resister in circuit. Its completely unnecessary any way, any arduino made in the last 5 years (The Uno) will have one on board, already wired and working. Its usually labelled 'L'. The tutorial you've found is out of date and doing it today can damage the Arduino. You may have already damaged the output on Pin 13.