Here are a few forum scripts that are free, just go to their sites and find the downloads of them:
http://mybboard.net/
http://www.phpbb.com/
http://www.simplemachines.org/
Those are the top three free forum scripts. Go into their "communities" to see their forums in action and what they look like. There are also skins for each forum, so if you don't like the look, just remember that there are other styles.
The two top forum scripts out there are:
http://www.vbulletin.com/
http://www.invisionpower.com/community/board/index.html
vBulletin and IPB are pay-to-use scripts though. You have to pay quite a bit of money to get them.
These are the steps to go about when installing a forum:
Download the file package. Extract it on your computer and upload the files to your site with an FTP Client. Either that, or you can zip up the group of files and upload them via the file manager in the control panel (this is a much easier way in my opinion. Remember to check the "Unzip files after upload" box though!)
Now create a database. In your control panel here on ULMB, there's a database section. Go in, give it a name and give it a password. Remember this information!
Now run the installation by going to :
"yoursite.ulmb.com/install/"
It really all depends where the install file is though. Sometimes you can just go to the site itself :
"yoursite.ulmb.com"
And it'll redirect to the installer.
Fill in the information during the installation. Remember that the host is "mysql" not "localhost" !!
Put in your database information. Username and Database name is the same. Password is what you gave it.
Just continue on with the installation and everything should go just fine.

If you have any issues or need help installing a forum you have in mind, just reply and I'll help you out further