You can organise private vehicle transfers to Malatapay costing around Php1400 per trip (1-5 people) or you can take the ceres bus from the bus terminal in Dumaguete (short walk from ferry trike ride from airport) the ceres bus goes every half an hour and costs Php30 per person and finally there is the Jeepney that have no set schedule and you can catch in Dumaguete centre for Php 20 per person.
The boats that cross to the island are called 'pump boats' and come in two
sizes small and very small, this is a typical very small pump boat from Malatapay,
there are two ways to take the trip, between 2 and 3 pm each afternoon is
a loosely scheduled boat costing Php 300 per person each way, it only seats
4 (although they often put 6 or 7 people on board) and it goes when its ready
(the return trip form the island departs between 6 and 7 in the morning same
fare), catching this boat is a little hit and miss and only goes once a day.
The other way is to hire a pump boat for the trip which cost Php2000 per boat, and will cross at any daylight time, it should be yours but they tend to let Apo islanders sneak on if there is room.
While you are waiting for your boat ride across I can highly recommend a small cafe right on the beach at Malatapay where the boats depart from, its called Dream Beach Cafe and offers great food, friendly service and they have lots of information about boats, buses and the local area.