[I would use the whiteboard to draw diagrams as I was talking]
A good analogy for circuits is that of water pipes. The wires are nice wide pipes with no resistance to flow. Resistors are sections of narrow pipe that restrict flow. A pressure difference (a.k.a. voltage) is needed to push water through these narrow sections. Really small pipes require high potential differences to push water through at the same rate - this is the origin of the equation V = IR.
What would happen if you get two pipes next to each other? [work through logic with student: answer is that the effective pipe width doubles]. The "effective pipe width" is called conductance, and is equal to 1/R. From the diagram, it is clear to see you simply add these conductances together, which is what you do in circuits: 1/R = 1/R1 + 1/R2. This will give you the overall conductance, and you take the reciprocal to get the resistance!