What exactly are surface charges and what do they do?
You may find this document helpful, since it seems to be the primary source for the popularization of this idea. The short version is that the battery creates an electric field which pushes on the electrons in the wire. The field looks vaguely like this:



According to the above source, calculating surface charge distribution is extremely difficult. But if you look at the direction of the field lines and imagine your wire imposed on top of it, you can see that the electric field is going to be pulling electrons away from the left side and pushing them towards the right side. The surface charges eventually distribute themselves so as to create a uniform electric field throughout the wire:


  Ultimately, this elegant negative feedback mechanism will produce an arbitrarily complex distribution of surface charge all over the wire such that the electric field due to all the charges (surface charge plus the charge on the [voltage source]) is uniform throughout the wire and has the magnitude predicted by conservation of energy (the Kirchhoff loop rule).