OK, as you have chosen to post on this particular forum you are suggesting that you want to code your own rather than use a third party service like Bravenet.
You cannot use html to build a forum you need to use a server side programming language.
1. Find out which language your hosting service supports, if any. Most free services do not support server side scripting
2. Take some classes in programming
Frankly unless you are studying computer science or are a professional building a forum for a client (in which case you wouldn't be asking here) it is far better to sign up for a service such as Bravenet. Whoever you sign up with they will host the forum on their own servers and will provide you with a url so you can link from your site.
If your hosting supports PHP and mySQL (eg. Bravenet Premium hosting) then you could use the free forum script from http://www.phpbb.com/
If your hosting doesn't support server side scripting and a database then a third party hosted solution (eg. Bravenet forum service) is your only choice.
