You can visit the beach for free, but it's well worth paying for a boat trip.
We chose the amphibian boat tour, which takes you on a 40 minute trip amongst the icebergs. If you're feeling brave, you might prefer the zodiac boat tour. Being smaller, zodiacs can get even closer to the ice and explore more of the lake. You also get a bit longer, with tours lasting an hour.
Our guide explained that the ice was over 1000 years old, and the black markings were due to ancient volcanic eruptions. He then scooped a chunk of ice out of the water, and asked if we wanted to taste it.
You're allowed to scoop icebergs out of the water and eat them
Be warned, the boat trips only run until October or November, and may be cancelled in bad weather. If the boats are finished for the year, you might consider taking a tour of the ice caves instead.
Before you leave, don't forget to walk down to Diamond Beach, which is where the lagoon meets the sea. The beach is usually covered in chunks of melting ice, and this is where the best photos are taken.