I'm an electronics noob. I have this string of LEDs but don't know how to connect them to my Arduino Uno. As they are wired in parallel, there are two wires / four ends. What do I plug where?
Connect the negative ( or cathode ) to ground ( 0V ) and the postive ( anode ) to the output pin of the controller.
Firstly connecting that many LEDS directly to a single micro pin is not a good idea. Usually you would need to go through a buffer/driver first which can deliver the correct power to the LEDS.
I'm not that familiar with the UNO but unless that board has a driver circuit on it you might need a few extra components.
What are the specs of the LEDS?