There are significant dialectal differences between the islands and the following phrasebook is based on the dialect of Ishigaki, the largest and most populous island. See the separate Yonaguni phrasebook for the version spoken on Yonaguni.
A few examples:
English Ishigaki Shiroyasu Yonaguni
Sea Tumoːrɨ Inaga Unnaga
Head Tsuburɨ Amasukuru Mimburu
Cloud Hwumu HwumoN Mmu
"j" is pronounced like a "y" in English. Some syllables begin with a "ng", and this may be difficult for some English speakers. The triangular colon indicates a long vowel.
There is a very, very large dictionary you can get at some bookshops, it comes in two volumes, one Yaeyama->Japanese and the other Japanese->Yaeyama. It also includes a brief grammar.