You need to find a place to host your site. You probably will need to run a test file and see how much space you will need first. You can then look for a site that meets your needs. There are a number of free hosting services and many specializing in genealogy. Then you will need an FTP program to upload the files to the site.
Some sites have uploading utilities built into their utilities that work from web pages.
Cyndi's List has a number listed as do many of the shareware and freeware sites on the internet. Once you have the site uploaded and are comfortable that it is working properly and ready to go you will want to make some efforts to register it with gendex and some of the search engines. Good instructions are provided for this in the two sources mentioned previously.