One of the best ways of curing a sunburn fast is to apply a cool compress to the sunburn as the cool compress will help to cool the sunburn off and then you should apply some Aloe Vera Gel to the sunburn.
Massage the Aloe Vera Gel into your skin over the sunburn which will help to reduce inflammation of the skin.
I've also heard that mixing some Apple Cider Vinegar with some water in a spray bottle and spraying the Apple Cider Vinegar on the sunburn can help soothe the sunburn and make it go away much faster.
You can also add some Apple Cider Vinegar to some bath water and soak in the Apple Cider Vinegar bath to help soothe the sunburn and make the sunburn go away faster.
Oatmeal also works to soothe skin problems so you might try soaking in an oatmeal bath when you have sunburn.