The golden rule is to think as though you're in a kitchen. If it feels like you'd bake your meal in a oven, grill with the lid on. If you'd fry it in a pan, then grill it with the lid off.
Hose down your grill and lid, inside and out, to rinse out any residual ash. Deep cleaning Now start scrubbing. If you use dish soap, scrub the entire firebox and grates with hot, soapy water ...