One of the most respected web directory is Open Directory, Dmoz.
Some of the major search engines also have their own web directories. Until this year (2011) Google had it own directory but also used information from Open Directory.
In order to have your web site accepted by a Web Directory you need to submit the site on-line. At some point a directory editor will visit and evaluate your site. They then decide whether or not your site will be included in their directory. Once a web site has been accepted it is listed in a specific category. Users can browse through these categories or search using a keyword. In most cases in order to submit a site you need to find the category that fits your site and submit the url from that page,
Open Directory, Dmoz, originally Gnuh which became Know How and is now owned by Netscape (AOL). GnuHoo was originally started in 1998 in response to the frustration that many people experienced in getting their sites listed on Yahoo! Directory. Open Directory listings are maintained by volunteer editors who visit the web site and after evaluation decide whether or not it will be included in their Directory. Robozilla (a computer program) then periodically visits and flags sites which have moved or no longer exist. Editors then follow up to check the sites again and take action.
Submit Your Site to Open Directory
You can submit a site for inclusion at Open Directory at: http://www.dmoz.org/help/submit.html.
When submitting a site you need to select a category then submit your site. Submitting a site to Dmoz does not guarantee that your site will be accepted. At some point one of their editor visits your site and hopefully sometime later includes your site in their directory. Once part of Open Director's index your site is perodically visited by Robozilla a spider written to check the status of all sites listed in Open Directory.
Submitting a site to Dmoz does not guarantee that your site will be accepted. Open Directory does not charge for listing your site.
Getting Results or Not
Dmoz says that it takes about 2 weeks for your site to be visited and evaluated but it can take a lot longer. Actually trying to get your site listed can be a very frustrating experience and it will probably take a lot longer than two weeks, the main reason for this is that they only have so many editors. Each editor handles their own category and although some categories have very few requests others have massive backlogs. One of the main problems with this directory is that you are not notified if your site does not pass muster. Even your submission is not acknowledge.
There are numerous web directories most of which charge a fee to list your site. Here are three of the most well known and popular.
Yahoo - Directory - Submit to Yahoo - Yahoo started out as a web directory and although they are now a search engine they still maintain their directory. They charge a fee to review your site the fee does not guarantee that your site will be listed
About in addition to being a web directory they give a ton of information on numerous topics
Lycos also gives a lot of information in addition to the listings. Submitted listings are through advertisements.