There are two daily flights between Reykjavík’s domestic airport and Vestmannaeyjar (from around 17,000kr one way) on Eagle Air.
Eimskip’s ferry Herjólfur sails from Landeyjahöfn (about 12km off the Ring Road between Hvolsvöllur and Skógar) to Heimaey year-round. The journey takes about 30 minutes. You must always reserve ahead for cars, and passengers should book ahead in high season, especially at peak day-tripper hours: the morning to Vestmannaeyjar and the afternoon back. You must arrive at least 30 minutes before departure. Landeyjahöfn ferry terminal has vending machines, bathrooms and water, but no other services.
From 15 May to 14 September five boats depart daily, plus one extra service on Saturday and Sunday. Low-season boats function on a reduced schedule (usually two per day). Fares cost adult/child from 1380/690kr. Bicycles cost 690kr each, cars under 5m cost 2220kr. You can change your ferry time for a fee of 500kr.
In really foul weather (summer or winter), the port at Landeyjahöfn can fill with sand, in which case the ferry may instead sail to/from Þorlákshöfn on a reduced schedule of two per day. The journey takes 2¾ hours, and the fare is substantially more. Changes are posted on the website and Facebook page, and you need to check on your rebooking. It takes roughly two hours to drive from Landeyjahöfn west to Þorlákshöfn.
To get to/from Landeyjahöfn, you can take Strætó bus 52 from Reykjavík's Mjódd terminal (4600kr, 2¼ hours, three daily in summer). It stops in Hveragerði, Selfoss, Hella and Hvolsvöllur. There's a local Landeyjahöfn taxi service.