Directories are different from search engines. You usually have to pay for directories.
You can submit your url to the search engines, but the fastest way to get picked up these days is to have a link to the site on some other relevant site or page.
I have a site that went from 1-5 visitors per day to over 100 visitors per day in around 6 weeks and is now Alexa ranked and yesterday when I checked it has placed about another 500,000 places better than a few weeks ago. Hopefully it will keep doing better, funny thing is it's just a free 5 page starter site that I've neglected.