There are so many ways of building a web site but what you need to understand is that a domain name and a website are not necessarily the same. First you cannot get domain names free, not TLD's any way (.coms) You can get a free co.cc name http://www.co.cc
Then you need to know if the site you are going to build with allows you to use this name. A proper domain name will allow you to log in and set the nameservers to the company that is hosting your site, check before building a site if you can use your own domain name or not. Both paid domain names and co.cc free names can be used with any hosting account. You could use free hosting http://www.4fr3.com this hosting control panel allows you to either upload your own sites or choose from hundreds of templates and simply edit them, or you could install your own forum, cms site, pic site and a host of others from the auto installer. When signing up with foreverfree your first domain name will be your www.username.4fr3.com but once the account is set up (instantly) you can add up to 6 domain names and 6 subdomains so you get 12 webistes from one account. You could have www.yoursitename.co.cc (or com if you purchase a name) then www.forum.yoursitenaame.co.cc (a sub domain) you would need to spend a bit of time understanding the control panel but there are tutorials and it's not complex. After signing your site is instantly on line at the username you chose .4fr3.com eg: www.cal.4fr3.com and all sub domains are instant. Add on domains are created instantly but take time to propogate the world wide web, that's true for all domain names on all hosting accounts.