TTL is a factor that gets put into play after you browse your site. Here's how it works. You browse, your ISP gets the domain-ip resolution and stores that in its cache files for the pre-determined TTL, as long as no one using your ISP browses your site again in that TTL then it gets dropped.

so if you change your IP and then browse your site, you will very likely get to your new server. But if you browse, then change the IP, then browse again, you will get to the old server.

And to make things even more fun, every time you browse a site that is cached in your ISP's local caching servers, the TTL gets recalculated and reset based on a bunch of factors that are too boring to bother getting into right now. Plus there is also a max TTL factor that states that after so long they have to refresh the IP address lookup.

Anyway, short answer is within 15-30 minutes

cheers,
Luke