A proof-of-principle electron electric dipole moment (e-EDM) experiment using slow cesium atoms, nulled magnetic fields, and electric field quantization has been performed. With the ambient magnetic fields seen by the atoms reduced to less than 200 pT, an electric field of 6 MV/m lifts the degeneracy between states of unequal lbar mF rbar and, along with the low (approximately 3 m/s) velocity, suppresses the systematic effect from the motional magnetic field. The low velocity and small residual magnetic field have made it possible to induce transitions between states and to perform state preparation, analysis, and detection in regions free of applied static magnetic and electric fields. This experiment demonstrates techniques that may be used to improve the e-EDM limit by two orders of magnitude, but it is not in itself a sensitive e-EDM search, mostly due to limitations of the laser system.