Electric field from conductive to dielectric media I am interested in the main difference between transitions from electric fields from Conductive to Conductive/ Dielectric to Dielectric and Dielectric/Conductive media. 
What are the boundary conditions that an Electric field and a potential has to fulfill?
I think I only know it for dielectric to dielectric media, where the potential has to be continuous and the electric field changes by the amount of surface charge. 
 A: These boundary conditions depend only on the charge distribution of the boundary and can be obtained directly from Maxwell's equations.
The quantity that really matters is the total surface charge density at the boundary:
$$\sigma_{total}=\sigma_b+\sigma_{free}$$
In the boundary of two dielectrics, each dielectric will cause a bounded surface charge density of $\sigma_b =\mathbf{P}.\hat n$. So in the boundary of two dielectrics:
$$\sigma_b=\mathbf{P}_1.\hat n-\mathbf{P}_2.\hat n$$
In the boundary of a conductor and a dielectric you will have a surface charge density caused by polarization of the dielectric and also a surface charge density to make the electric field zero in the conductor. (static case, as is your question tagged)
The following is the most convenient form when dealing with conductor to dielectric boundaries:
$$\mathbf{D}.\hat n=\sigma_f\tag{$\sigma_f$ is free charge density}$$
So the quantity that really matters is the charge distribution of the boundary.
And in general when you have a surface charge density of $\sigma$ , the boundary conditions will be:
$$V_1=V_2$$
$$\mathbf{E_2}.\hat n-\mathbf{E_1}.\hat n=\frac{\sigma_{total}}{\epsilon_0}$$ 
