Turn off the power to the kitchen exhaust fan at the breaker box or fuse box.
Remove the fan cover. Some are removable some aren't so don't try to force it, you may break it. If it is not removable use a sponge dipped in hot water and ammonia to wipe the outside thoroughly. If the cover is removable, soak the fan cover in a 50-50 solution of hot water and ammonia. Make sure to wear rubber gloves and work in a well ventilated area. After soaking for 15 to 20 minutes scrub with a soft bristled brush and dry thoroughly. Do not use any abrasive cleanser or steel wool, you will scratch the finish.
Unplug the fan, remove it and put it on an old towel or newspaper. Wipe with a clean dry rag to remove excess grease and dirt. Use a sponge dipped in hot water and ammonia on the fan blades, use care not to get the motor wet. Dry thoroughly.
Remove any filters and soak in a grease cutting dishwashing detergent and hot water for 10 to 15 minutes. Rinse filters thoroughly with hot water and dry.
Reassemble the exhaust fan and switch the power back on.