This website will walk you through the basics. Why does it matter? Why learn how to do it at all? I've got grammar checker. That's all I need. Right?
Wrong. Tools are only useful if you understand them. Would you try using a router when you had no idea what it was supposed to do? A multimeter is just a weird device until you understand what it's measuring and how to use it. Grammar checker is only a tool. When you understand how grammar works, you understand how limited a tool grammar checker really is.
Diagramming sentences is also a tool. It can help you better understand language. It can help you construct sentences that are more clear and more elegant. It will improve your writing.
Why bother? Because language is communication. Writing is a method of transferring ideas from my head to yours. If my writing is unclear, because of poor grammar or spelling or misuse of commas, the idea isn't going to transfer correctly. What I say and what I meant to communicate are at odds with each other.
Language and grammar are the tools a writer uses. If you improve your understanding of the tool, you improve the end product.
Besides, sentence diagramming has its own kind of beauty, almost like poetry or math. I'm thinking of drawing a nice big diagram of a very complex sentence and framing it for my wall.