First, find your screen. Look underneath your stove vent and find the mesh that covers a good portion of the area underneath. Normally it is held in place by a slot at the back and a small plastic lever or knob in front. On mine a simple quarter turn releases the front and a simple tug pulls it out of the slot at the back. I try and handle it by the edges since it's going to be covered in grease to some extent. You could wear rubber gloves if it's really nasty. Put some paper toweling on your work-space and lay it down on it. It could be quite dirty and you don't want to have to clean grease off any other surface.
Once out, you'll be able to see how much crud it has accumulated on both sides. I've found that if you fill up a basin or just the sink with a couple of inches of nice hot water and a good grease cutting dish soap you can soak most of the crud away without resorting to scrubbing. After it's soaked for a while, I usually use a long bristle brush to do a "once over" to make sure everything is loosened and then a rinse with hot water will clean the rest. Make sure the water runs clean before you put it aside to dry. It may need more soak time and a bit of additional brushing.
***A word of warning! Do NOT do this in your RV sink, remember that sink feeds into your grey water tank so all the grease and other stuff will end up coating your tank. This is in no way a good thing. It could smell REALLY bad, or begin growing some flora you really don't want to have to clean out!! At the very least it will coat your sink drain pipes and make a mess in there. If you do gunk up your pipes, do NOT use a harsh chemical drain cleaner in PVC pipes. It will not end well. OK Back to the regular scheduled cleaning. There could also be "chunks on the screen. Make sure all of them are off!
Once done, air dry the screen on a dish towel (wipe it a bit if you wish.) While it's drying, I usually wipe down the fan blades with a paper towel sprayed with a household cleaner. Wipe GENTLY and don't bend the blades. Most of them are just plastic and can be brittle if they are getting up there in age. (Don't I know that feeling!) I also wipe down the underside of the vent, as best I can, to get any remaining grease or splatters clean. I'm always surprised how far cooking splatters will fly. I mean it's at least three feet from the pan and I've found chunks of past meals up there. Yuck!
This should take about ten minutes or so, less if you do it regularly. You'll also notice an increased efficiency in airflow when you use the stove vent. In the spring (Maybe sooner) I am going to retrofit the old, noisy and power hungry fan with a 12 V "computer type" muffin fan. I'll get more flow with MUCH less noise and less power draw. Always a good thing! Of course, I'll write it all up!
Be Seeing You...Down The Road,
Rich "The Wanderman"
www.thewanderman.com