This sort of journey leads to true invention. In seeking to build something you don't understand as a whole, you must explore the underlying components. And when you find the bit you need that hasn't been built yet, boom! Invention!
Moreover, this is how most 'puzzle' based interviews are done.
I've said this before, and I don't think it's any big secret, but the silly questions you hear in interviews almost never care about getting the right answer, but test to see if you can work a process to at least get to a plausibly believable answer. Or at least that's what I've always looked for when interviewing.
I remember asking a guy "How many jellybeans can you fit into a school bus?", and he started working the problem out. He guessed at the dimensions of a jelly bean, then asked me something about how many cubic feet are in the interior of a school bus, then began working out the problem mathematically.
This was exactly the right process, at least by my estimation, though there were other really interesting ways people approached the problem. A surprisingly large number of people just said "I don't know", without bothering to go any further, and one guy even got mad at us being one of those "stupid puzzle shops" and left in a hurry.
The reason I remember the one guy though, was because at the end, he asked me something like "I think the answer is such and such, with an approximate margin of error of 10% or so. How close am I?" When I confessed that I had no idea what the answer was, and that I was really just looking to see how he came up with the process, he laughed louder than I've ever heard anyone laugh ever before. I told him his guess was likely closer than anything I might have come up with on my own, and we eventually hired him and he proved to be great.
The skills necessary for good problem solving are myriad, but at least to me (and apparently Justin Kan), it starts with breaking problems down into bite-sized chunks. Another big thing for me (that I didn't see in the article) is in asking questions for things you don't know. Nobody knows everything, and I've found that the best engineers I've worked with have always been pretty systematic about clarifying things they weren't clear on. That's huge too. If you need to know whether we're talking short bus, field trip bus or regular old school bus, ask. An answer for one is probably not the answer for another.
I think building a (successful) start-up is a lot like getting a PhD. You make a bump on the circle at some point: http://matt.might.net/articles/phd-school-in-pictures/