Soldering wires to a 5V-to-12V converter
On the PCB to the left, there is no label of "negative or positive". How can I tell where to solder the red (positive) and black (negative) wires. 


I would use a voltmeter. Or you can tell by traces on the PCB itself. The input and output sides have a common ground. So the trace that goes from the input (USB connector) straight to the output, that is ground (negative pin).


  Furthermore, on the PCB to the right, it says the output is "5-16V", even though when I bought it the description said 5v to 12. I am a bit confused.


That means that the chip used is capable of supplying 5V to 16V. Usually it requires just a change of resistor value. But you are right, it is confusing.


  What is the proper way to solder a red and black wire to the output "holes". 


It doesn't matter as long it is soldered firmly. It just depends on how you need it, which side.