What is an expression for the output voltage?
The circuit is linear with ideal sources, so the output voltage is the sum of the contributions from all the different sources.
To calculate the contribution from 1 source, replace all voltage sources, except the one from which you want to determine the contribution to \$V_{out}\$ by a short circuit, and all current sources (I know, there are none, but this is the general procedure), except the one from which you want to determine the contribution to \$V_{out}\$, by an open circuit.  

In your example this boils down to first (1) short circuit \$V_4\$, then $$V_{out_1}=\frac{1}{3}V_3$$Next (2), short circuit \$V_3\$ and see that $$V_{out_2}=\frac{1}{3}V_4$$.
Now the result is the (linear) sum of both: $$V_{out}=V_{out_1}+V_{out_2}= \frac{1}{3}(V_3+V_4)$$.

The reason that voltage sources are replaced by short circuits and current sources by open circuits, is that an ideal voltage source has zero impedance, so in fact it would already be a short circuit if the voltage were zero.
An ideal current source on the other hand has infinite impedance, so that if its current is zero, you're left with two open terminals: an open circuit.

So in fact you just summate the effect of each source on the variable you want to evaluate while keeping the circuit exactly the same: all but one source values are zero for each contributing source.