A passport is all you need, but you have to have it.
One tip: If you walk around the island, you will probably go by the school. A few inexpensive school items would be appreciated, such as children's books, pencils, crayons, paper, notebooks, ballpoint pens, etc. It is quite primitive by our standards, so anything in that order would help.
All that you need is a passport. If you would like to get your passport stamped with a Kiribati immigration stamp, take it ashore with you and you will find the immigration officers under the large banyon tree to the right. They will stamp and sign it for $1.00.