Is it really as simple as ticking off all the verbs and nouns and other types of word?
Additionally: Where can I find a clear and easy to understand dictionary of grammatical terms and descriptions? I know the difference between a transitive and intransitive verb, but I can’t seem to spot them in context.
Of course I didn’t expect you to do that. It is totally pointless if you do it by hand. Instead I wanted to (ab)use this as an opportunity to mention that there are more interesting aspects to analysing sentences.
Since last fall I am a student of computational linguistics (switched over from computer science.) While we do not usually diagram sentences according to this specific method, some comp. linguists really work on the analysis of the structure of sentences. One goal is to enable a computer to parse a natural sentence and infer the correct structure automatically (and for a computer using the context is much harder.) This is absolutely crucial for many natural language applications (e.g. automatic translation…)
Btw. when I went to school only very passing reference was made to diagramming sentences and more formal grammar teaching was mostly limited to our Latin classes. Apparently diagramming was a rather traumatic experience for many Americans
There’s no one way to diagram a sentence–there’s not even any discreet way; all the theories run into each other. If you really want to know (or want to be convinced that you really don’t want to know), maybe check out Andrew Radford’s two textbooks in the red Cambridge Linguistics series; one on transformational grammar, and one on minimalism.