I scoured the internet for instructions, and I found several different methods, including using a hot glue gun and a stapler. However, I opted to use the method that looked closest to my aunt's, which can be found on YouTube here.
Don't forget to work outside to avoid the fumes!
Start with 50 nine-ounce plastic tumblers. Heat up the soldering iron and melt holes in the bottom of all 50 cups. On my first try, I made the holes too large. Making them as close to the size of the light base as possible will make them more secure when you insert them later.
Not-so-great first attempt:
Much better second attempt:
Next, make a circle of 12 of the cups, and temporarily secure them with clothespins. Use the soldering iron to melt through the cups and hold them together. I found it best to squeeze the bottoms of the cups together and melt my holes at the base. I figured this out on my second try. The first time, I tried melting them together on the sides and that did not work as well.
Once you have the first ring built, remove the clothespins and then start building the top rings. Build the first half using this method, and then repeat to build the second half.
Now it is time to add the lights. Working in a zigzag pattern, place one light in each hole. I used LED lights, and almost all strands come in 60 count. My first try, I made two holes in ten of the cups so that I would use up all the lights. However, this made it difficult when it came time to put the two halves of the ball together because I did not have any extra length to work with. So on my second attempt, I left the extra lights loose in the middle and gave myself a little extra breathing room when adhering the halves together.
A side note... The first ball used a set of mini twinkling lights that I had on hand. Although the end product was fine, the mini lights are not quite long enough to stay securely in the holes, so I have a few empty cups. The longer, regular size lights work better.
Once you have all the lights securely in the holes, put the two halves of the ball together. I secured them with the clothespins until I could melt them together. And that's all there is to it. It's really simple and the end result is really pretty.