You must arrange for transport from one of the local boats to come and retrieve you for a fee. It is a several mile trip in an outrigger canoe with outboard motor over open water, swells can be large and you can expect to be sprayed with saltwater throughout the trip (wear sunglasses). The boats will generally meet you at Zamboanguita where the Malatapay Wednesday market is held. Take a jeepny from Dumagete, just ask the driver or the guy who collects fees off the back of the jeepny to warn you when it is your stop. It can also be arranged through Apo Island Resort to go from Dumagete to Malatapay-Dauin, and from there directly to the island.
If you want to stay near the pier in Dumagete, the Coco Grande Hotel is only 1 minute away.
The island is only 3 km around and 120 m high at the top of the hill, walking will get you anywhere you need to go on the island, including to the top of the hill.
One of the Philippines' famous diving sites, Apo Island has one of the world's best known community-organized marine sanctuaries. It is home to over 650 documented species of fish and estimated to have over 400 species of corals.
Diving and snorkeling are the main activities around the island. Resorts on and off the island typically hold diving programs for different skill levels. Instructors are commonly PADI-certified. The diving is excellent, plenty of reefs, tons of fish and turtles-amazing visibility. Keep an eye out for the Giant Trevally which is known in these waters.
There is a dive-shop on the beach, single dives generally go for around $25 USD inclusive of gear.
There isn't much in the way of retail on Apo Island. It is advisable to bring anything that you may need with you because it is a long trip back to Dumagete. The local women will try to sell you t-shirts and kitsch when you arrive and when you leave.
Both hotels have restaurants, Liberty's has particularly good chocolate/banana shakes. Menus are limited but what is available is pretty good. At Liberty's, the dive master will go table to table during dinner and help you arrange the next day's dives.
Several beach resorts at nearby towns regularly offer trips to the island, and it is more common among divers and tourists to get accommodations off Apo Island. Examples of hotels outside Apo Island are Thalatta Beach Resort in Maluay Zamboangita, Bahura Resort & Spa in Dauin and Wellbeach Resort www.wellbeach.com . Rates span from budget to splurge, with some hotels usually offering a range of activities that explore the mountains, water falls, sulfur springs and other beaches of Negros Oriental.
There are only two resorts on the island, Liberty Community lodge and Apo Island Beach Resort.
Liberty Community Lodge  is the larger of the two, it has a very nice restaurant and both private and dorm type rooms. The private rooms are situated in what appears to be a large expensive private house, the showers use barely desalinated water and the island is always on restricted water use.
Apo Island Beach Resort is on the opposite side of the boulder from Liberty Community Lodge.
Apo island is generally the place to get out too, Dumagete is the city to get to Apo from. Here  is a good write up on the island.