For my generation, sentence analysis—a grammatical exercise that pretty much died with my age group—was called diagramming, but older folks knew the same exercise by the name parsing. Whether you call it diagramming or parsing, it's a skill that can save your life when you're an unmotivated undergrad who has to slog through sentences written by thinkers who have been dead for centuries.
Over at his fine blog, Malcolm Pollack has slapped up a quote from Edmund Burke's 1790 Reflections on the Revolution in France, a tract that was written while the French Revolution was still in medias res. I Googled a sentence from Malcolm's blockquote and found a fuller version of the text (here). On that webpage, I saw the following sentence, whose grammatical complexity made me grin:
When the old feudal and chivalrous spirit of fealty, which, by freeing kings from fear, freed both kings and subjects from the precautions of tyranny, shall be extinct in the minds of men, plots and assassinations will be anticipated by preventive murder and preventive confiscation, and that long roll of grim and bloody maxims, which form the political code of all power, not standing on its own honour, and the honour of those who are to obey it.
Think back to your undergrad years, when you would be put to sleep by sentences like the one above. The reason such sentences were (and maybe still are) soporific is that it's hard for modern people—who are used to shorter, more direct sentences—to figure out the core meaning. But my contention is that, if you know how to parse a sentence, you can figure out rather quickly what the sentence is trying to say.
For study purposes, the only thing that's really important—and I used to say this to my high-school charges back when I was a tutor at YB—is to figure out what the simple subject and simple predicate are. Know those things, and you've got the essence of the sentence, no matter how tangled the full sentence may appear. So let's look at the above locution, palpating its fearsome length the way Dr. House might gingerly palpate a stretch of small intestine.
The sentence begins with "When," which is a subordinating conjunction, so we already know we're going to be dealing with a complex or a compound-complex sentence, i.e., a sentence with at least one subordinate (or dependent) clause in it, and therefore also one main (or independent) clause. So: at least two clauses. By staring grimly at the sentence and frowning mightily, I see that that clause's simple subject is "spirit," and the simple predicate is "shall be," followed by the predicate adjective "extinct."
So: partly decoded. When the spirit shall be extinct...
This brings us up against a comma, and the comma alerts us that we're now, very likely, going to plunge ahead into the main clause. With that in mind, what are the simple subject and predicate of that clause?
SUBJECT: plots and assassinations
PREDICATE: will be anticipated
Later on, there's a comma-and locution that might fool us into thinking that yet another clause is about to rear its head ("..., and that long roll of grim and bloody maxims..."), but if you look carefully, you see there's no predicate, for where's the verb?
What we have now, stripped to its barest essence, is this:
When the spirit shall be extinct, plots and assassinations will be anticipated.
To make the word "spirit" a bit less vague, we can reincorporate the descriptive phrase before it in order to clarify:
When the old feudal and chivalrous spirit shall be extinct, plots and assassinations will be anticipated (by preventive murder and confiscation).
This is the 18th century—the Enlightenment era—so a notion of "feudal spirit" would already have been centuries old (the High Middle Ages will take us back to, oh, the 1200s or so—half a millennium en arrière). The tone of the sentence is wistful and thus probably conservative. "Lose your old values, and everything will go to hell" is what this sentence is saying.
Parsing is a skill that can save your bacon when you're an undergrad slogging through a densely written text. For young, modern minds that are impatient, and that want to cut right to the essence of a sentence, parsing is an invaluable skill, and it's a shame to know that most American schools, in their haste to do away with all things grammatical/structural and to embrace all things holistic/contextual, don't teach this skill anymore.