If you are comming by car, easiest way would be to drive to Split and then take Split - Stari Grad ferry. Once on Hvar, follow signs to Vrboska, but turn left when you see a sign for Basina.

Alternatively, you can drive few miles more to Drvenik and then take a Drvenik - Sućuraj ferry. Once in Sućuraj, take a road to Jelsa, Stari Grad and turn right when you see a sign for Basina.

Taking an aeroplane or a train to Split is also an option but you will need to take a taxi once you arrive to Stari Grad ferry harbor.

Drvenik - Sućuraj ferry line
Departures from Drvenik every day at 0:30, 5:45, 7:30, 9:00, 10:30, 13:00, 13:30, 15:45, 17:15, 19:00, 20:30 and 22:30.
Departures from Sucuraj every day at 0:01, 5:00, 6:30, 8:15, 9:45, 11:00, 12:30, 15:00, 16:30, 18:00, 19:45 and 21:30.

Split - Stari Grad ferry line
Departures from Split every day at 1:30, 5:00 (6:00 on sunday), 8:30, 10:30, 14:00 (15:00 on saturday), 17:00 and 20:30.
Departures from Stari Grad every day at 5:30, 7:30, 11:00 (12:00 on saturday), 13:00, 17:30 (18:30 on saturday), 20:30 and 23:00.

If you are comming by boat, you can anchor in the Basina bay, and you're only few steps away from the Ivelja house.