First of all I want to make it clear its not totally free, you have to pay the domain name fees and hosting charges, but the script is free, thanks to phplink directory.com.
Phplinkdirectory provides a free directory script which can be easily installed and maintained by anybody. Just visit their site, register yourself and download the free script. The free script has certain limitations, obviously, nothing is actually free in the world, but for a start, its a good script to rely on. Now register a good relevant domain name like web directory and buy a small hosting package. If you want me to recommend one I would certainly go with hostgator.com. I have been using for the last 5 years and it is excellent, fast, secure and easy to setup.
Now you have the domain name, hosting package and the free script. It's time to explain how to make a web directory. At first think about the topic of the web directory. Will you make a general web directory or a niche? If you ask me I will recommend you to create a niche, since there's a lot of general web directories and its very very hard to compete with them at first. So go for a niche which will be less competitive like fashion, car accessories, travel, shopping etc. Choose a topic that interests you, write down in a few words about your directory in some place on the homepage. Then create categories relevant to the topic of the directory. You can get some ideas about the topic if you go through google directory, dmoz or yahoo directory. Dont just copy their categories, create something unique.
Now add small descriptions to every category which will help your category page to rank higher in the search engines. Google loves content, the more the better, but it must be unique. Dont copy paste the category descriptions from other directories. Now search a good template for the directory, you will get a good no of free templates for phpld or other scripts. Or you can pay a designer to make a unique theme for your site.
It's almost over. Now let others know that you have launched a new directory. Promote your directory in forums like digitalpoint, namepros, vilesilencer, v7n, there are many. And dont forget to build backlinks. Quality backlinks can take your directory in a better position in search engines. No more tips, it's time to start to make your web directory.