The best way to see the erupting volcano on the Reykjanes Peninsula is with a Guided Volcano Tour. Included in the tour is transport to and from the volcano. A professional guide will lead you on the hike to the eruption site and provide you with crampons if needed. They will then show you the best spots around the flowing lava for you to take amazing photos while still being safe.
There are other active but not erupting volcanoes in Iceland. Most located under glaciers or in the Highlands. The best way to explore these is also on a guided tour.