From what I've read (which includes a Smashing mag article and an Akamai article) implementing HTTP2 server push consists of simply adding a header or two to the pages on my website. For example:
Link: </css/styles.css>; rel=preload; as=style
Link: </js/common.js>; rel=preload; as=script
Is this accurate? Is it really that easy?
It depends entirely what web server you are running and how it implements HTTP/2 Push (if it does at all).
Using Link Headers works for Apache for example. Server push is not currently supported for Nginx. Some CDNs implement it with Link headers too.
However even if it is that easy to enable, you probably shouldn't without further thought. The problem is that while this will probably speed up the first load, and your JavaScript and CSS will be cached after that (you are caching your resources client side aren't you? If not then don't even look at advanced topics like HTTP/2 until you get the basics right). So if you push when its already cached it's a waste. Now a browser can stop a push, if it doesn't need that resource, because it already has it like in this example, but that still takes time and effort and for small resources (like CSS or JavaScript) it will likely have pretty much downloaded by the time you stop it.
So you should only push when there's a high chance the client will need the resource. Cache-Digests will be a way for the client to tell the server what resources it has cached, and so help the server to decide whether to push or not, however it's still a work in progress and not away if any browsers supporting it yet. In the meantime I've a simple cookie-based implementation here done in Apache, that might be of interest to you: https://www.tunetheweb.com/performance/http2/http2-push/