I read science magazines (SCIENCE NEWS especially) regularly and understand all the articles in them. I understand the principles of mechanics, even though I cannot do any of it. I've been learning wood carving and wood turning and talk regulary with my brother who is learning machining and understand all he discusses, and as soon as he gets set up for full projects, I will work with him.
I am a draftsman by trade, and have a rudimentary understanding of engineering practices.
In science fiction, a solid science knowledge is quite useable. If you know something about science, you can bluff your way through a story involving technical concepts.
If you have read several hundred or more science fiction books of various kinds, you will know what is acceptable science practices and can bluff your way through copying their practices.
Of course, the type of science fiction you write will effect how much science you really need to know.
If you write Hard science fiction, like Asimov, Clark, Heinlein, you will need a well developed science background.
If you write light science fiction such as where the character and intereactions are key and the science fiction is strictly background and the main character does not understand the technology, then one can get away with very little science fiction background.
Of course, one can go with Science Fantasy, such as Star Wars or Flash Gordon, and get away with little or no real science knowledge.
In an Windows XP environment, I wrote a rudimentary chess program in Visual Basic, tic tac toe, and Pacman (enough of it anyway to where I was satified I could do the rest).
Professionally, for the last ten yeared I've work with MVS Mainframes. JCL, COBOL, SAS, VSAM, DB2 ect... application programming with no bells and whistles.
Now I regret going into this line of work because its dying. At least, in the US. _Oh the joys and wonders of globalization and how its everything the ever so wise economists said it would be!_ Underscores=Sarcasm
To tell the truth, now that I'm approaching 35, and life is busier than ever(aka my new hobby is writing), its lost its magic and wonder. I hear the hard drive cycling and wonder what in the world Windows is doing behind my back. So I am not as savvy as I once was in the good old days of DOS when the computer did what I told it and only that.
Fortunately, for the kind of writing I try to do, the technology I understand is more important than the technology I don't.
[This message has been edited by J (edited December 15, 2006).]
For everything else---a great deal of general knowledge, and occasional depths of it, too. But no systematic study.
This extends beyond science. For example, I know an apallingly great deal about the Beatles and am usually on the lookout for more. (Just yesterday I learned the name of the dentist who...well, if you know the Beatles you'll know what incident in their lives I'm talking about. And if you don't care, it doesn't matter.)
"Caring" is pretty much how I learn all this stuff---I'm interested, I dive in, and days or months later I emerge with a bunch of trivia that, strung together, might add something to my store of knowledge.

Just kidding, of course I don't make it do everything it could do. It could operate a point defense cannon, but do you think I'm going to give up my cycles to something like that when I could be playing games? So not going to happen. Mechanical traps are just fine for my needs.
Do I have a "deep" understanding of technology and how it works?
That depends on what you mean. I understand quite a bit about how technology develops and interacts with a community of adaptive organisms. I also have a high degree of machine empathy, I can often fix minor problems simply by using my chi, and most machines work better the longer I interact with them. Electronics particularly, but also things like motorcycles and lawnmowers. And of course I've studied transistor based logic gates and can design and build a simple ALU, memory registers, io devices, and software using various computer languages.
Yeah, and I love cheating at computer games. Not in multiplayer, it's already unfair enough without that. But I like peeking past the interface and looking at the raw data, yeah. It also helps to remind the computer who's who to whom.
Inkwell
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"The difference between a writer and someone who says they want to write is merely the width of a postage stamp."
-Anonymous
http://www.soul-of-the-machine.com
Music created by the ghost in the machine.

I was more thinking along the lines of primary domain controller, but a defense cannon way cooler. So those of you who understand technology, how does it affect any of your writing? Do you mesh concepts that you understand in with the narrative in some way?
Complicated stuff, I know.
I think anyone's expertise affects their writing. The more technically minded people, in my opinion, are more apt to produce very structured stories. Not only thinking of myself, but other author/technical minded people, sush as, Asimov, Clarke, etc., all have very structured, logical stories. Not that that's bad, it's just a style. The stories, for the most part, are still very fasinating and can contain a good deal of emotion, action, philosophy and whatever else ... they're just more structured and follow a logic progression. At least, that's what I see in my writing and in other technically minded people.
I have a habit, though all novice writers do I'm sure, I just seem to have it more so, spewing out a couple of terms or ideas that make perfect sense to me, but utterly confuse my eaders. Mostly surrounding tech.
What does that mean? I have no idea. I've been at work too long and I'm just starting to babble.
Anyway, my formal technical training is focused more on electronics, particularly communications and information systems. But my raw empathy with machines isn't a trained thing, it's apparently something I've had since pretty soon after birth.