How to picture sinusioidal wave in transmission line(electrical circuit in general) ?
It's not very clear what your friend doesn't understand, but what you said is correct.

In a conductor like your transmission line, there are a number of free electrons, with enough energy to be outside the atoms' orbitals and in a state called "conduction band". these electrons are vibrating, or moving in a more or less random fashion. But if you look at them as a whole, they're on average still.

If you apply an electric field, they will be attracted by the point with the highest potential (they're negative charges) and away from the lowest. Therefore they will start drifting in that direction. Note that this movement is slower than the actual speed of the electrons, but still pretty fast: still in the order of magnitude of the speed of light.

An alternate voltage switches polarity following a more or less sinusoidal waveform. This means that the high potential changes from one side to the other. So the electrons will start drifting in one direction, than slow down until they're still again, and then reverse. Depending on the frequency of the sinusoid, they might actually never leave the cable, but if you're observing a section of it, you will see the oscillation.

If you add reactive components, the story gets a bit more complicated since they will affect the "sync" between the field intensity (voltage) and the flow (current).