Dish detergent and water, then wipe off with a damp cloth. Allow to dry and repeat if nessassary. Use a soft brush on the grill. If you have access to an air compressor you can remove the grill, apply your cleaner, let it soak to loosen the grime then use compressed air to blast off the residue. After you get the dirt and grime off, coat the vinyl with a protectorant (Armor All or similar product) and if the vinyl is discolored a coat of shoe polish will sometimes restore both the color and luster.
If the amp is that dirty on the outside, you should also use compressed air to blow out all the dust and cobwebs on the inside too. It wont hurt to give the pots and plugs a cleaning with a deoxidizer while you are at it.