Note:You can't use fishing line. Don't even think about it. It just doesn't conduct light in the right way.[ref]
You can buy optical fiber by the reel, but there are better and cheaper ways to get it*: For large star maps; a fake Christmas tree works very well! This time of year, it's not hard to find one cheaply.
For smaller star maps; the retro-tastic 'UFO Lamps' are a great source of fibers, and are pretty easy to find in dollar stores.
Both of these sources are great! They are cheap, and they terminate all the fibers into one place, so it is easy to light the stars.
* The more stars you have, the better it will look. Try to find a tree or lamp with plenty of 'points'.
* The size of the tree/lamp will determine how large your map can be. For example, if you have a 120cm / 4ft tree, you can build a map about 2m / 6.5ft wide. (Of course, the exact shape of the tree and your frame will affect the maximum. Get your measurements right before you buy/cut anything expensive. ;-) )
[*] Some fiber-by-the-reel is sold here. The 0.5mm fiber is probably the closest to what is found in trees/lamps, and costs 8c/ft, or 2c/ft if you buy 19,680ft worth. A $5 UFO lamp might have 400 x 1ft strands, already cut and terminated - at 1.25c/ft.