What is the best way to soothe a sunburn?

Not much: Apply moisturizing lotions to keep it from drying, and this will help some. Aloe is considered helpful by some. If you have actual blistering, then this is a second degree burn, and should be treated with an antibiotic cream-neosporin- until it heals.

Sunburn care: I agree with dr. Sexton. Apply cool compresses. Aloe vera (aloe barbadensis) can reduce redness, pain, itching & swelling from a burn. It has anesthetic, anti-inflammatory & antibacterial / antifungal qualities. It can speed burn healing by stimulating growth of new skin. Non-steroidal anti-inflammatories and acetomenophen can be very helpful. Hydrate well and don't peel off any deep layers.

Simple Care: Sunburn is response of the tissues to injury from solar radiation. It is simply inflammation which means increase blood flow to the area to promote healing. Do not use ice as this can injure already injured skin. Cool water soaks can help as can taking anti-inflammation medicines like Motrin or advil (ibuprofen). Avoid any further damage as this can cause scarring . Good skin cream applied daily/gently helps.