Look here for basics https://youtu.be/c7HXLl8YREM
I'm not sure I agree with the quote though. It so happens that the websites I linked all had an element of playfulness, but I don't think that's required.
Here's a site I worked on. Check out the hover animation for the four tiles underneath "Our Innovative and Customer-Driven Businesses": https://web.archive.org/web/20190610202159if_/http://2018ar....
IMO, there's nothing playful or "humorous" about this animation. I would describe it instead as "elegant"—it gives the site an extra level of sophistication.
Another (very small) example might be the "Apply Now" button on https://www.airforce.com/