It is hard to tell how it is wired in that pic, but if it really is just two long copper wires with the glowing glue blobs every few inches between the two wires, then it appears to be a large parallel array of single LEDs. I don't know how they handle current balancing that way, though... Depending on what your options are for powering this, it may be a smarter idea to run them in series so that each LED sees the same current and lights up about the same brightness.
But yeah, looks like thin enameled wire, LEDs, and some hot glue or something.
Edit: It looks like they actually might be wired like christmas lights. Wiring in series would be easier for DIY, but series-parallel is doable too. Series-parallel allow you to have more lights on a single string, but makes wiring a bit more complicated, and would also need toincorporate a current-limiting resistor for each series string that is paralleled onto each other.
http://buybuyskyimg.tallgame.com/product/LDEST-9087_D_05.jpg
Here's a closeup of one of the blobs. Might be a resistor under the LED, hard to tell for sure. It could just be a really tall blob of solder.
Here's a super easy LED wiz that can help you get an idea of what you can do
http://led.linear1.org/led.wiz
Typical small white LEDs you can approximate as:
Vf (forward Voltage) = 3.3V
I (or If, forward current) = 10mA
Set your source voltage to whatever DC source you will be powering it from.
You might consider checking e-bay, as these light strings don't look all that expensive, but you could DIY if you have the time and steady hands.