The easiest way to Siargao Island is by plane.
Cebu Pacific Air has been connecting a while Cebu City and Siargao Iceland. There are 2 flights per week, they are currently Mondays and Fridays.
You can also fly daily to Surigao. Cebu Pacific and Philippine Airlines offer flights.From Surigao you can go by boat to Dapa (Siargao port). Several ships go from 6 clock in the morning.