How do I connect this string of LEDs to my Arduino Uno?
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?