Most skin electrodes use a conductive gell to keep the electrode to body resistance low and constant. Otherwis the electrode noise is larger than the body signals.
Methods to remove EMI from the power line radiation are used. One is to use differential signal electrodes. Another is to have a common mode electrode on a different part of the body.
The amplifiers should have low noise and high input impedance and low bias current.
You may need to use DSP or other filtering methods to block out all frequency ranges not involved with the desired signal.