As a website admin, you can request an IPv6 address, configure your webserver to listen on it, and configure your DNS with an AAAA record for it. ie. you can make your website accessible over IPv6.
However, depending on your business, you might want to be careful. At a minimum, clamp the MTU on the server to be less than 1500. There is still a fraction of clients that will be broken by this process.
I run a small service which you can try on your website "right now" and see what happens, without affecting your users too much: http://testv6.stdio.be/
I could except my hosting provider still isn't ready - apparently their data center itself isn't totally ready. I was told 3 months ago to check back in 6-9 months.
