Here is a light made from a plastic bottle, fishing line, an old USB cable and a slow colour change RGB LED.

The nylon thread (fishing line) does not have quite the same effect as real optical fibres. There is more light signal degradation along its length so it doesn't have the same bright point at the end of the fibre. Although the diffusion of light along its length still looks kind of neat.

I included an optical fibre that I plucked from my Christmas tree as a comparison.

Step 1: Materials:

small plastic bottle
nylon fishing line or jewelry thread
usb cable
5mm RGB slow colour change LED (I got mine on eBay) and a resistor
spout from a cooking oil bottle
paint
pebbles
clear drying glue and clear packing tape
twist ties
plastic bottle with desired circumference (see step 4)

Tools:

pliers
scissors
paint brushes
soldering iron
glue gun and glue
ruler and measuring tape
something sharp to use to poke a hole in the plastic bottle.

Step 2: Preparing the Base

I used an aspirin bottle (about 10 cm in height) as the base for my little light, you can use pill bottles, small water or juice bottles, whatever you can find. I was lucky to have a spout from an olive oil bottle fit perfectly on the aspirin bottle. Alternatively (if you are not as lucky as me in having a perfectly matching spout for your bottle) you can cut a hole (approx. 1cm in diameter) in the lid of the plastic bottle.

Remove label and adhesive from your plastic bottle, if you have trouble getting it off you can try a product like Goo Gone.
Near the bottom of the bottle poke a hole through the plastic for the USB cable to fit through (from my pictures you can see that I made the hole after I painted -that was not a good idea because I had to go back and touch up the paint).
Paint the bottle, I chose black because I didn't want any light from the LED to seep out the bottle. Apply several coats if necessary.

Step 3: Preparing the Light

For the light source, I used a colour changing 5mm LED, it was quite bright (4000mcd) so I just used one LED. Bearing in mind that the USB cable when plugged in to a computer gives 5 volts of electricity, use the appropriate resistor, by calculating the value with Ohm's law (R=V/I) or use a web site like Current Limiting Resistor Calculator for Leds

USB cable

Cut off the extraneous end of the USB cable with pliers.
Peal back insulation, exposing the wires underneath. Cut off the green and white wires.
Removing the plastic casing at the ends of the red and black wires.

Before soldering, feed the USB cable through the hole in the base.

Soldering

If you are just using one LED, solder the red wire to one end of the resistor.
Solder the other end of the resistor to the positive leg of the LED (this is the longer leg).
Solder the ground leg of the LED (this is the shorter leg) to the black wire.
Test it out -plug your cable into computer to make sure it works
Trim off excess wire and wrap it up with electrical tape.

Step 4: Preparing the Fibre

Cut a bundle of nylon fibres to 10 cm in length. This can take a long time if you just measure and cut. An easier way of doing this is to find a plastic container (plastic is better because it will be easier to slip the scissors under the nylon to cut) with a circumference of 10 or 20 cm*.

Cutting

Tape one end of the nylon thread/fishing line to the container.
Wrap thread around bottle, many times, don't worry if some of the treads overlap the length doesn't need to be exact.
Cut across the length of the threads (see image below), hold the bundle together with twist ties.
Repeat until you have a large enough bundle of nylon thread, I did it 3 times.

Memory

Nylon tends to hold it shape when cool, this is referred to as line memory. So when it is wrapped tightly around a spool and waiting for you to wander into a store and buy it, it will take on the shape of the spool. So rather then having a nice straight thread/fishing line it comes out in curls. I had this problem with my jewelry thread, to remedy this; place the bundle in a shallow bowl and pour boiling water over it. Allow the water to cool. The nylon will become straight.

Trimming and gluing the bundle

Use several twist ties along the length of the bundle to keep all of the threads together

take the bundle of nylon threads and cut in half, so that they are approximately 10cm in length now.
take one end of the bundle and try to line up all of the threads as best as you can. With scissors trim off about 1/4-1/2cm so that the end is even.
pour glue into a small cap (I used the cap from the water bottle) and dip in the end of the bundle that you just cut. Allow excess glue to drip off.
Take a strip (~2cm in length) of packaging tape and wrap it tightly around the glued end of the bundle.
Allow the glue to dry, then trim off any excess tape so that one edge of the tape is flush with the end of the bundle.

*I originally planned to use 20cm as the length of the thread, but then I thought it would look better shorter, so I cut them in half!

Step 5: Putting It All Together

Use a twist tie to hold the nylon bundle of thread in place with the taped end in the spout (or lid, if that is what you are using), apply glue with a glue gun around the bundle, fill in the gaps and make sure it is secure.
Paint the over the area you glued.
Drop some pebbles into the base of your light. When it starts to get full, manoeuvre your light into place. Make sure it centred and just under where the nylon bundle will be.
Fill the bottle the rest of the way up (~3/4full) with the pebbles to keep the light in place.
Place spout/lid on the base and plug into computer, dim the lights in the room and enjoy the pretty colours.