How LONG does it take a spider to find a new site?

That's a tough one to answer!

It depends on how new your site is, how many incoming, high-quality links you have to your site, what niche your site is in, and so on.

A great way to increase the speed with which your site is found is to have many high-quality incoming links to your site. Use GoogleBar (a free download from Google) and find sites with high "Page Rank" and ask for links. A great start is to get listed in DMOZ.org, a free Yahoo-like directory that Google uses for all its directory searches.