How does measuring the location of one entangled photon affect its pair? If you have two entangled photons that are moving in opposite directions and you measure the location of one of them, what happens to the wave function of the location of the other photon?
 A: Nothing happens to it. 
If you know how the two photons are entangled, and if that entanglement has anything to do with the locations of the two photons, then you now know what would happen if you tried to measure the other photon's location in the same manner. This is possible because you combine the measurement result with your prior knowledge of how the entanglement is set up. If you don't already know how the two photons are entangled, then you cannot derive any information about one photon from measuring the other one. 
Entanglement is a property of a system as a whole, and so the information derived from it comes from prior knowledge of the system, rather than any kind of communication between the components due to measurement.
A: For two entangled particles there is only one wave function, the wave function of the entangled system. It is not the case that each entangled particle has its own wave function. If you want to say there is such a thing as the collapse of the wave function, then when you measure one of the particles, the wave function of the system collapses, so now you have information about both particles. To give a concrete example lets consider the case of two electrons in the singlet spin state with wave function: 
$$|\psi\rangle~=~\frac{1}{\sqrt{2}}\left(|+\rangle|-\rangle~-~|-\rangle|+\rangle\right)$$
Then, for example, if you make a measurement of spin along the z-direction, your state will "collapse" to either $|+\rangle|-\rangle$, or $|-\rangle|+\rangle$, meaning, that if the spin of the first electron is $+1/2$, the spin of the second will be $-1/2$, and vice versa. Everything works out fine, and there is no mention of a wave function for each electron, which is the same as saying that an entangled state is not a tensor-product state, it cannot be separated into two independent states.
