We have obtained data for 41 star forming galaxies in the MUSE Atlas of Disks(MAD) survey with VLT/MUSE. These data allow us, at high resolution of a few100 pc, to extract ionized gas kinematics ($V, \sigma$) of the centers ofnearby star forming galaxies spanning 3 dex in stellar mass. This paperoutlines the methodology for measuring the ionized gas kinematics, which wewill use in subsequent papers of this survey. We also show how the maps can beused to study the kinematics of diffuse ionized gas for galaxies of variousinclinations and masses. Using two different methods to identify the diffuseionized gas, we measure rotation velocities of this gas for a subsample of 6galaxies. We find that the diffuse ionized gas rotates on average slower thanthe star forming gas with lags of 0-10 km/s while also having higher velocitydispersion. The magnitude of these lags is on average 5 km/s lower thanobserved velocity lags between ionized and molecular gas. Using Jeans models tointerpret the lags in rotation velocity and the increase in velocity dispersionwe show that most of the diffuse ionized gas kinematics are consistent with itsemission originating from a somewhat thicker layer than the star forming gas,with a scale height that is lower than that of the stellar disk.