Conversion to/from the user’s script is supposed to be done by the browser.
This has existed for quite a while, the new thing is that previously the TLD (i.e. country code) still had to be the old ASCII ISO code. Now even the TLD can be encoded, so that it will display in the country’s native script. So far there are 3 non-ASCII TLDs registered (that is, in the DNS they are still ASCII using puny coding).
Related: I recently put together a package for iPhone developers that adds some support for IDN to NSURL (this code will be deployed in the next update of Twitterrific for iPad). http://files.iconfactory.net/sean/NSURL+IFUnicodeURL/
Icann warned that the internationalised domain names (IDNs), as they are known, would also not work on all PCs immediately.
"You may see a mangled string of letters and numbers, and perhaps some percent signs or a couple of "xn--"s mixed into the address bar," said Mr Davies. "Or it may not work at all."