To learn a language or culture, it is easier to start listening to the song.
I find several YouTube posting of Hainan songs. You may click the followings and enjoy listening to them. SuukeeMei from Malaysia is particularly talented and champions the use and speaking of Hainan dialect.
海南歌曲Suukee Suukee You can access to her 24 YouTube video files there.
2005年之《 家在马来西亚》 you know more about suukeemai
海南小品 《琼香茶店》 with caption
黃明志 - 史上第一首海南RAP SuukeeSuukee by Namewee
海南伯父 (高飞) 57 VIDEO
海南話拼音語音教程（t） a little boring, but very useful and thorough.