[Arakon]

two possibilities:
you use IDE wires, and cut off all but 3 strands inside. then twist the remaining three tightly together and tin them. that makes them pretty much exactly as wide as a chip pin.
best way is to hold it to the pin and heat it up above the pin, the solder will melt further down the wire too and attach to the pin.

or you get 0.1 mm thick copper wire, the kind that is covered in some sort of clear paint, and solderable.. I'm not sure what the english word for it is. that's easier to solder, given your soldering iron tip is small enough, but also easier to break since it's so thin.

both types can be gotten at good electronics shops.