There are daily direct flights from Honiara to Munda (1.2hrs flying time), or via Gizo or Seghe (both centres nearby).

There is an overnight ship which sails from Honiara to New Georgia Island (Seghe & Munda) one a week, however, conditions on board are very low standard & the vessel can be very over-crowded at times.  Safety conditions are questionable...much safer to fly.