The lesson I learned from this site was to break problems down into the smallest possible sub-problem. I was failing because I was trying to build two lists next to each other with add and remove and clear all functionality, and I was trying to build all of these features at the same time.
After stumbling for awhile, I realized that I simply needed to be able to add and remove from a single list. Then the next focus was having two lists on the page, one of top of the other. The final step was to get the lists next to each other.