How Do I Use jQuery UI In My Plugin

It’s a sad day in the world when I Google something and it returns nothing. I am trying to use the default datepicker (or ANY datepicker at this point) and am unable to because of my lack of knowledge with WordPress/PHP. In my plugin, I am attempting to register jquery and the ui and apparently am breaking other parts of WordPress in the process. Can someone please tell me what I’m doing wrong and if they can provide a working solution, I will scrap all of my code: