I would like to know how I would go about purchasing a ferry ticket from Naha to Taketomi. Do I first have to travel to Ishigaki?There is no direct ferry service between Naha and Taketomijima, and no longer ferry service between Naha and Ishigaki. You will have to fly to Ishigaki first and then take a short ferry to Taketomijima.
http://www.japan-guide.com/e/e7202.html
If so how would I then travel on to Taketomi?
From the airport take a short taxi ride to the boat terminal where you can catch a ferry to Taketomijima.
http://www.japan-guide.com/e/e7201.html
http://www.japan-guide.com/e/e7250.html
Also, how much would the fair be and how long would the trip take?
Flights between Naha and Ishigaki are about 20,000 one way and takes about an hour. The ferry to Taketomijima is 1100 yen one way and takes 10 minutes.