In an antenna how fast do electrons move when receiving a signal? In an antenna how fast do electrons move when "receiving a wave"?
 A: They move at the drift velocity for that material and that electric field. A strong FM radio signal from a nearby station has an intensity of about $10^{-5}$ W/m^2, while for a weak astronomical radio source it might be more like $10^{-26}$ W/m^2. The equation for the drift velocity in terms of the intensity $S$ is
$$v=\mu \sqrt{\frac{4\pi k}{c} S}$$,
and if we put in a typical electron mobility for a metal of $\mu\sim 3\times10^{-3}$ m^2/V.s, the results range from $\sim10^{-8}$ m/s for the weak astronomical source to $\sim100$ m/s for the strong radio station.
I'm surprised that the OP accepted the answer by Bill N, which seems to me to be  uninformative.
A: Assuming you are talking about a simple dipole-style antenna, either half-wave or quarter-wave. The electrons will be induced to move in a fixed-phase relationship with the fluctuations of the electric field. Based on the length of the antenna and the angular frequency of the wave you can estimate the electron speed by using the time derivative of $$x(t)=A\cos(\omega t + \phi_0).$$
$A$ depends on the type of antenna.
