If you want a really detailed answer, you will need to be a lot more specific, you should include all the info you can about the parts (like the part numbers, and datasheets for the parts, does the string use LED drivers? What LEDs, an what are their voltage and current ratings? are the drivers supported on the arduino?
You may want to start with a small project, like a little matrix or cube, to learn about multiplexing and charlieplexing.
You could use wifi or bluetooth, or maybe IR to send data if you can not physically connect the arduino to the LEDs, but that will require a lot more hardware, and bring the cost and complexity (difficulty) up quite a lot, which is probably too much for your first project.