Hargray is the telephone company for the island. I just look under "Internet Service Providers" in the Yellow Pages once we get to the room and call them directly (.35 per call or use your cel phone). They have a special rate for vacationers and will set up your account in about 10 minutes.
Each dialup connection is .35 for members. There are a few national ISP's available - they do have local numbers for AOL if you want to load up a free trial version of that service - but then you have to deal with pop-ups and other intrusions for months afterwards.
As noted, there are also providers with 1-800 numbers, but for $10 the local service is pretty simple.
Enjoy!