Charge near conductors
Here, we consider what happens when charges are near conductors. For instance consider a spherical neutral conducting shell with a point charge Q placed in the center.
The field inside the shell must be the same as for a free charge, because a Gaussian surface I can be drawn around the charge, inside the conductor, and the field leaving must be given by Gauss's law.
Inside the conductor the field must be zero because there are never fields inside conductors. Therefore if I draw Gaussian surface II, I will see that the net charge inside the surface must be zero, hence there must be a charge -Q spread among the inside surface.
Finally, since the object is neutral, there must be a charge +Q on the outer surface.
Whenever confronted with such a problem, work from the outside in.