Amanohashidate JR Pass

Hi,

I plan to go to Amanohashidate but how do I do so?
With JR pass I must the extra amount right? Do I get off at Fukuchiyama and buy train tickets? Or do I get off at Amanohashidate and pay there?

I plan to go to Amanohashidate but how do I do so?

Of course, it depends on where you are coming from. Here are some basics:
http://www.japan-guide.com/e/e3991.html

With JR pass I must the extra amount right?

Yes.

Do I get off at Fukuchiyama and buy train tickets? Or do I get off at Amanohashidate and pay there?

There are a few direct trains from Kyoto. If you ride one of them, you do not need to get off at Fukuchiyama. In all other cases, you have to change trains at Fukuchiyama and will pay the ticket for the non-JR train at the separate ticket gate at Fukuchiyama Station. If you ride the direct train, then you usually pay the supplement on board of the train to the conductor. It may also be possible to buy the supplement ticket in advance at the ticket counter, but I am not sure.

If - for some reason - you end up not paying the supplement until arrival in Amanohashidate, you will be asked to pay it at the ticket gate of Amanohashidate Station.