How are wingtips attached to the aerofoil while maintaining structural rigidity?
There are a number of winglets available in market for retrofitting and their method of attachment will also vary. Boeing details the procedure for attaching a winglet to their BBJ and it is quite instructive. According to the article the main issue is modifying the wing to accommodate the winglet, rather than the attachment itself.


  The more time-consuming part of the retrofit is installation of the
  wing modification to accommodate the winglet.


For this particular aircraft, the following steps are given:


  
  Removal and replacement of the outboard upper and lower skin panels
  Removal and replacement of rib 25, which is third from the outermost rib
  Installation of stiffeners across rib 25.
  Cutting of the closure rib (rib 27) and trimming of the two spars
  Installation of the new center section of rib 27 and the
  new winglet attach fitting 
  Installation of the spar attach fittings
  Installation of the aft-position light.
  


which is followed by installation of the winglet.



Installation of winglet, from Boeing Aero.