Getting to Abemama requires planning. The only regular connection is by air from Tarawa, the capital of Kiribati. Air Kiribati operates infrequent flights on its small inter-island aircraft — schedules change and seats are limited, so book well in advance through the Air Kiribati office in Tarawa.
Inter-island cargo ships also visit Abemama periodically, but their schedules are unpredictable. The journey by sea takes roughly half a day from Tarawa. This is the cheaper option but requires flexibility and patience. Ask at the port authority in Betio (South Tarawa) about current sailings.
There is no international gateway on Abemama itself. All visitors arrive via Tarawa, which has an international airport with connections to Fiji and Nauru. Factor in at least one or two nights in Tarawa before and after the Abemama visit, as connections can be unreliable.