We stumbled upon this by accident, one of those "let's see where this goes" kind of things. I don't know why this and Kirkjufjara Beach isn't more famous, the views from here are amazing in every direction, and it's different everytime you visit. Probably the place we visited the most in Iceland. It's only a short drive from Reynisfjara Beach.
Coming from the ring road, just follow the sign "⌘ Dyrhólaey", after a few minutes the road might just be covered with water as it's on almost the same level of the road! It's almost always safe to just drive through it, even if you don't have a 4WD. Just follow the road until you see a gravel road on your right side. It goes up pretty steep so don't go too fast.