A ferry called Herjólfur, operated by Eimskip (http://eimskip.com/EN/ice...), runs between the mainland and Vestmannaeyjar. Recently a new harbour was created in Landeyjar, shortening sailing times significantly, but as it frequently fills with sand the old harbour at Þorlákshöfn is also in use. Add to this the fact that high waves often occur on the route and you get very irregular travel times, so it's best to check the status of the ferry before showing up at the pier! If you're traveling by car, it can also be brought to the islands with the ferry.
As in the rest of Iceland, public transport can be quite difficult to navigate and cannot take you everywhere. However the bus system is slightly more developed in the south and there is a bus that travels daily along the entire southern section of the ring road. There are also buses that travel between the upcountry towns in the western part of the south. Most of these are operated by Sterna (http://www.sterna.is) or Reykjavík Excursions (http://www.re.is), but it may also be worth it to ask around locally as there may be different seasonal options.
The south is well served by the ring road, which goes right through the region from west to east serving most of the population centres on the way. The western part of the south is one of few regions in Iceland where populated areas are found far inland, and this area has a good road system as well. Further east the interior turns into highlands and glaciers, and should only be reached by 4x4s.