How to Create a Forum

Register a domain (or subdomain) at a PHP host.
Download PHP forum software.
Download an FTP Client and use it to upload all your PHP content to your host.
Create a MySQL database on your host through the control panel.
Go to yoursite.yourhost.com / forumdirectory/ install.php to install and configure your forums.
In your FTP client, go to config.php > Properties and set the CHMOD settings to 666 (if you are using phpBB 2).
Follow the instructions on install.php.
After finishing installation, go to the CHMOD settings of config.php again and set them to 644 (if you are using phpBB 2).
Delete the install and contrib directories.
Go to yoursite.yourhost.com/index.php.
Login and go to the admin panel to customize your forums.

Another perspective:
1. Choose a Forum Topic
2. Choose a Domain Name and Forum Name
3. Web server that supports php & mySQL
4. Set Up a Hosting Account
5. Install Forum Software
6. Configure Forum Settings and Permissions
7. Upload Forum Themes and Mods
8. Monetize Your Forum (Optional)
9. Create Forum Categories and Boards
10. Spread the Word

Reference:
http://www.phpbb.com/
http://www.simplemachines.org/

phpBB is good for free forum software
vBulletin (3.0) is amazing, and if you want to have real control over the forums is worth the cost. The admin CP is incredible.