Welcome to the forum! I am by no means an expert at lighting starship models, but I know the fundamentals. Maybe I can help you.
Will any-old fibre optics as sold at my local electronics store (primarily as data cable) do?
Some types of data cable will work, but IMHO they are not the best solution for lighting a model. I think what most of us use is "unjacketed" fibers. These are usually plastic, not glass, and much cheaper. Look here:
http://www.fiberopticproducts.com/Unjacketed.htm
I got a big bag of this stuff many years ago from American Science & Surplus. The little "fiber-optic art" lamps at Wal-mart have a generous amount of these fibers in them.
What's the best way to "source" the light? I understand running 100 different strands all over the place etc, and having them come back to a single source, bundled together, but how then do I light them? Simply "point" them at an LED?
Here's something I like to do: use a short length of brass or aluminum tube as a collar to bundle the ends of the fiber together and insert an LED into the opposite end of the tube. Then tape or epoxy the assembly securely so that nothing comes loose. You can use telescoping tube segments to match the diameters needed on each side. Seems to work well for me.
Can you cover fibre cable on the flat? By that, I mean if you imagine a ruler, with fibre lying down it's length....could I duct tape it down, and as long as the ends are out it's ok?
Oh yeah, that's the beauty of the fiber. As long as you don't kink the strand, the light shoots though the length to the other tip. You can paint the shaft or tape it or glue it or whatever.
A neat thing you can do with the plastic fiber is to "lens" the tip to better duplicate the look of a spotlight. Hold the end near a flame for a few seconds and it will mushroom a little and gloss over, making a very convincing light. If you shine a very bright white LED though it, it will throw a lot of light. The beauty is that you can run a whole bunch of lights like this from a single 5mm LED. I lit up a Klingon Cruiser with just 3 basic LEDs: a bright white, a dim white, and a blinking red:
http://s101.photobucket.com/albums/m72/ ... n_0001.flv
Here's another hint: choke down the LED you're using to light your "porthole" fibers with more resistance to dim it down. This will help provide a sense of scale and differentiate them from brighter exterior lights.