Magneto-optical Kerr effect (MOKE) microscopy is a powerful imaging technique that can be employed to study the magnetization reversal of thin films and nanoscale structures. In this work, we describe the MOKE microscopy which is used to observe nanomagnetic domain structures of Co/Pt multilayers (MLs) and plot hysteresis loops. We were able to image sub-micrometer size magnetic domains and trace their evolution in a ms time scale with a lateral spatial resolution down to 300 nm. The magnetization reversal for Co/Pt MLs is described by the expansion of the domains in all directions as dendritic domain wall propagation. For a fixed applied magnetic field, the evolution with time of magnetic domains started from many centers, then expanded without the appearance of new nucleated centers. When the applied magnetic field was applied perpendicular to the film plane, a square hysteresis loop was observed indicating that the film exhibits a perpendicular magnetic anisotropy. For the same material, the magnetic field needed to nucleate magnetic domains in sub-micrometer size wire is much larger compared to the thin films. The magnetization decay becomes faster as the applied field is closer to the coercivity of the sample for the thin films MLs. The domain wall (DW) could be manipulated and pinned in a precise location in a stepped nanowire of Co/Pt MLs induced by a consistent magnetic field.