Do you know those nice guitar strings with a ball end (like this, for example http://www.frets.com/FRETSpages/general/glossary/BallEnd/BallViews/ballend.jpg ). You can re-use their end instead of pearls.
First of all save your old/broken/... strings and cut their end.
Decide what colours you're going to use.
Remove the string around your "bead".
Make a ring with the wire and leave around... 40 cm left.
Pierce the first bead.
Start wrapping the wire around the first bead, repeat for the other ones.
Now you should have something like the one in the photo.
Continue wrapping the wire over the beads... And you're done! :)