So, after some perusing, here's how you tell the difference: if the adjectives are supposed to be joined into a single modifier, hyphenate. For instance, if a kid is three years old, and you want to differentiate him from his older sibling, you'll write "the three-year-old boy." The kid isn't year or old, and calling him "the three boy" would confuse your readers. Because the modifiers only make sense together, you hyphenate them.
There is an exception to the above, and that's when the first word ends in -ly. The newly painted wall doesn't get a hyphen, because the reader will be looking for the adjective "newly" modifies. However, the just-installed door in the wall does get a hyphen, because the door isn't just.
For another example, let's say your protagonist went on a number of dates, and uses one major feature to describe each to her friend over drinks. The well-dressed one may well have made the best initial impression, and less if he were merely "well" or "dressed," both of which are a minimum requirement for dates. The tall and skinny one needs no hyphen, because both of these features can exist on their own. The Shakespeare-quoting man is indeed quoting, but what? And he's certainly not Shakespeare, unless that's the story you're writing. But would you really want to give it away so soon?
Basically, if you can remove either adjective, and it would still make sense, the most you'll need to do is a comma. If it doesn't make sense with any of the words removed, hyphenate.
If you're using a hyphen to separate, though, you're doing it wrong. The mark of punctuation you want to show you're about to introduce a concept is a colon ( : ). If you want to separate out part of the sentence in an aside, use an em-dash ( — ), which most word programs will automatically format from two hyphens put together ( -- ). If you're using Windows, you can also hold down the Alt key and type 0151 on your number pad. When you lift your finger from the Alt key, an em-dash will appear.
I've put spaces before and after the colon and em-dash, above, to make their appearance clearer. But when you use an em-dash, you don't put a space before or after it. As an example:
One might assume—correctly so—that I use em-dashes fairly often, if I have Alt+0151 memorized.I hope that cleared up a few things, and that I've managed to make hyphens not boring and easier to understand.