Fly into Split, preferably by the early afternoon at the latest. From Split one needs to get to either Hvar Town or Stari Grad on the Island Hvar:
You can take the Airport Bus (not the public transport) to the port and get a ferry or catamaran from there (schedule). The bus is 8 EUR. The choices from the port are the following:
A catamaran to Hvar Town is the fastest transportation, and it costs 10 EUR on Jadrolinija and 20 EUR on Krilo. These catamarans can sell out fast, so try to get tickets early or online. The trip is about 1 hour.
A car ferry to Stari Grad for 8 EUR. The car ferries are large and have a lot of space; they are also slower (2 hours). The ferries run frequently to Stari Grad, so you do not have to worry about missing one.
It is shorter from Stari Grad to the Institute than from Hvar Town, and the car ferry is more pleasant.