I am installing plug on my dishwasher. I know how to ground the plug but I don't know what to do with ground wire coming from the unit. Do I connect both wires to the ground screw?
Stop what you're doing and hire a electrician!
If you have to ask this kind of question here, then you shouldn't be messing with house wiring, especially with appliances that are likely to be in wet surroundings. You are in over your head. Have a professional do this so that you don't electrocute you or anyone else that ever walks into your kitchen.