The earliest taxi boat from Korcula leaves about 8 am and you can get a return from about 4 pm to 7 pm depending on season and weather.
Below are just sample prices – the actual fare depends on the type of boat, weather, and season. For example:
One way ticket for a taxi boat to Badija, Vrnik or any other islet in the Archipelago cost from 55 Kuna.
One way ticket for a taxi boat to Luka Korculanska beach is from 35 Kuna.
One way ticket to Lumbarda cost from 80 Kuna.
The best value option, in my opinion, is to take hop-on-hop-off 24 hrs taxi service and visit all islands in one day – all info is here
To take a water taxi you just turn up at the taxi boat pick-up point at East Port of Korcula (Punta Jurana aka Obala Korculanskih Brodograditelja), situated right next to Konzum supermarket and local bus stop, and jump into the first boat due to leave to your destination (map of Korcula archipelago)