If I apply $1 \text{ V}$ across a $1 \text{ }\Omega$ resistance, I'd get $1 \text{ A}$ flowing. $1 \text{ A}$ is defined as $1 \frac{\text{C}}{\text{s}}$, and $1 \text{ C}$ is equivalent to $6.24150975 × 10^{18}$ electrons.
Therefore, Ohm's Law describes only the number of electrons passing a given branch per second. How do we determine the speed of electrons as they move through a conductor? And what is that speed?
You can't measure speed of electrons from these data alone. If the area of the cross section of a cylindrical conductor is A then the formula would be $v = \frac {I}{QeA}$ where $Q$ is the mobile electrons per cc and $e$ is the charge of electron, $v$ is the speed of electron, $I$ is the current. This is for dc. See this http://amasci.com/miscon/speed.html
So you see, you need to know the diameter of the cylindrical conductor. However the electrons don't move in a conductor in an orderly manner. They are constantly colliding with each other and typically have speed components along the conductor about some millimeters per second.