Most people visiting Vestmannaeyjar travel by the ferry. It is a lot cheaper than travelling by plane, but it can be challenging for those who suffer from seasickness.
For me, I use a ferry every summer. Not to Vestmannaeyjar, though, I travel to an island on Iceland's Breiðafjörður Bay in the west called Flatey. The only way to reach this island is by a ferry (Vestmannaeyjar even borrowed said ferry while theirs was being repaired). I find the journey thrilling. I love standing on the deck and feeling the wind on my face. I love the view of the ocean and surrounding landscape. Sometimes I'll see white-beaked dolphins swimming along the ferry. It is an excellent way to feel connected to the Icelandic nature.