You can install your own normally by using ftp to get to your webspace. Good boards include this one (vBulletin), www.phpbb.com (phpB๐ and many others. I like phpBB because I have found it easy to install and customise. Once you have uploaded the files (normally lots so put them all in one folder eg. forum) you normally have to point your browser to a page like install.php. If you don't have ftp access I wouldn't reccomend this because forums normally have 100's of essential files, uploading through a web upload would be a nightmare and a half
! If so, I would then go for one hosted on another site (http://www.bravenet.com/webtools/forum/index.php) I am sure there are many listed on google aswell, however one that doesn't use ads of some kind will be quite rare to come by....