Sunburn can happen to anyone whether or not you apply enough of sunscreen or not at all. The point of sunburn aftercare is to prevent swelling and skin ageing.
First of all, an immediate cool shower can soothe the inflammation. Placing a cold towel on burnt areas will also do the trick. It is also important to constantly apply moisturizer or aloe vera to prevent peeling and dryness. Here's a tip: avoid using moisturizers that contain petroleum as it would trap heat on your skin. You don't want that!
Drink more water! Your body needs all the fluid it needs to keep you from being dehydrated. It is also very tempting to pop the blisters and peel off dead skin, but don't do it as it will cause inflammation and infection. It is a sign of your skin trying to heal, so let it be.