Anywhere between almost immediately and never.
Seriously, there is no standard. If the category editor is on top of things and your submission is on the up-and-up and there's not a huge queue and the moon and stars align in the right position, you can get in very quickly. If any of those things are not optimal, it can take longer. Sometimes a lot longer.
Best bet: submit and walk away. If you get in, that's great. If you don't, it's not worth losing sleep over.
BTW, you can still get to the Google Directory by typing in directory.google.com, but there's no link to it from the Google home page anymore. Not sure how long ago it's been since they refreshed from DMOZ.