The fastest and easiest way is by air. Cebu Pacific Air, Philippine Airlines (PAL) and AirAsia offer several flights from Manila to Panglao. Travel time is approximately 1 hour and 15 minutes.
You can also travel by boat. Tagbilaran City Pier is the destination of a number of ships from Manila. There are also ships from other parts of the Visayas, including Dumaguete and Cebu. If you are coming from Mindanao, you can board a boat to Bohol in Cagayan de Oro and Dipolog. There are also boats from Camiguin, but the destination is Jagna in the southeast corner of Bohol.