The shale shaker vibrate strongly and regularly in a certain motion, drilling mud from well head fall onto the shaker screen surface, separated under the strong vibrating force. 
While go pass the screen surface, water phase and clean mud fall into the mud system for drilling, solids separated and moved away for next process.
There are 2 eccentric blocks inside the vibrating motor, users adjust the angle of the 2 eccentric blocks to get different vibrating strength.
Note that: In drilling site, the 2 motors of a shale shaker should running under the exact the same vibrating strength for a stable performance.