Pull down on the cover in a gentle manner. If your exhaust fan model has pins on the side, press the pins simply to remove the cover. If there are screws that hold the cover in place, use a screwdriver to unscrew them.
Thus you can take the cover off entirely from the fan housing. Once the cover is removed, you can see the amount of dust and grim there which you are going to clean.
The crucial parts of the exhaust fan are the housing, motor and blades, and the cover. To resist unwanted grime build-up, you have to rinse every part thoroughly.