South Tarawa is essentially one long road running from Bonriki airport in the east, through Bikenibeu, Eita, Bairiki, and across the causeway to Betio at the western tip. Most travel is along this road.
Minibuses run almost continuously up and down the strip during the day. Flag one down, get on, hand the driver a coin or two when you get off. They are cheap, crowded, and the easiest way to cover distance.
Taxis are available in the main settlements but are not metered — agree the fare before you set off. Hotels can arrange a car and driver for the day if you want to do the battlefield sites without rushing.
To reach North Tarawa you take the road to Buota, then either wade across at low tide or hire a local boat. There is no causeway beyond that point and no scheduled transport, so plan accordingly and bring water and sun protection for the crossing.