It depends on google but normally within 30 days of submitting the site, and if you are placing you site in forums and directories even faster.
The OP said google DIRECTORY, as in the DMOZ clone. Getting listed in the ODP can take from a few minutes to a few years depending on several factors, and many sites never make it at all. Though once in DMOZ you can expect Google to update their directory sometime within a month to two years. Vague answers? Sure, but sadly they are true answers. To get listed in the ODP though, it's best to at least skim through their guidelines as they are not a listing service like so many other directories.
Hello... Do you want the truth or to be Lied to? Unfortunately unless you have a killer website that just "dominates" or you are willing to pay (bribe) someone whos in good with an editor then chances are "close to zero".... If i can make the suggestion that you submit and forget with DMOZ and just hope for the best and then start doing free and paid directories to establish a good ranking in the search engines. thx malcolm
ummmm.... what? Are you trying to say something that's not already been said within the thread already, or are ya just padding your post count? Though, I must say, in some cases it's just as fast, or even faster NOT submitting. But generally, yeah, you are correct... submitting your site to a directory is generally a good idea if you are wanting a fat listing.