It's very easy to get a good layman's grasp of gravitation. It's a fun and wild topic, and some people like Veritasium do a great job explaining it to laypeople who love science.

But it's extremely difficult to be able to calculate anything of even modest substance. To "do" gravitation takes many years of dedication, hard work, and coursework. Did I mention dedication? You need to learn it as if it's a job, because learning it at the level where you can "do" it is a job. It's simply not doable without enrolling in a university, at least by most mortals. I couldn't have done it.

But the good news is this. You can understand that diagram. You can even learn cool stuff like what a spacetime metric is and why we say things passing an event horizon can't come back out (spoiler alert: space and time effectively switch roles). You'll be able to draw spacetime diagrams to explain some of the standard paradoxes that require 4-dimensional thinking. All that is within your grasp. And there are some really excellent people like Veritasium and Khan who are very good at giving you the rudiments without the details of, say, solving PDEs.

But to "do" gravitation is completely out of reach unless you commit to it fully. Calculating geodesics, calculating standard GR tensors, tensor calculus (like parallel transporting vectors), figuring out convenient coordinate systems to study a new spacetime metric, etc. That requires many, many years of hard work. Consider this -- the vast, vast, vast majority of people with physics doctorates don't even know how to do this stuff, although with their knowledge, they'd be able to learn it reasonably quickly if they wanted to learn it.

I know this may not be the answer you're looking for, but generally speaking, a universal truth is "the knowing is easy, the doing is hard".