Standard Hydrogen Electrode
The SHE (Standard Hydrogen Electrode) is a standard equipment for measuring the relative electrode potential, as the process of measuring the actual potential is quite difficult. It consists of a platinum foil dipped in 1.0M $\ce{HCl}$ in the presence of $\ce{H2}$ gas at 1 bar of pressure.

Now when the SHE is connected to another half-cell, either oxidation or reduction may occur in the SHE. 
 
Suppose we have to find the electrode potential of a half cell represented by "A" Now, on setting up the cell and connecting a voltmeter we get the standard potential(Estandard) of the cell i.e.Estandard = EA - EH2
Now as our our aim is to just find EA, we take EH2 to be equal to 0
Therefore,
Estandard = EA - 0
or,
Estandard = EA

The value of Estandard is taken from the voltmeter.
It should be noted that the electrode potential calculated using this method is relative(to the electrode potential of hydrogen). It isn't the absolute value. 
Also, the potential for the SHE is taken to be 0 for the simplification of the process.