depends on what you want to do and how much you want to spend.
For example I use http://sites5.com/
to professionally host my site. I've played with several different forums to see what I like. For example most hosting companies provide "fanstico" scripts to install various software packages. Once you have chose a package and installed it then it is just a matter of setting up the site.
I have used drupal, simple Machine Forms (smf), php-nuke, and IPB. IPB (Innovision Power Board) is the best IMO but cost a fair amount of money. Drupal is free and open source. I find that it is fairly easy to navigate and use. If you have to go in and customize modules and so forth I found it easy to understand.
Here are two sites that are highly customized drupal installs: http://twit.tv/
I've been playing around with several different ones and recently went back to php-nuke. This is because I wanted a standard forum layout that was easy to admin and create content for. Drupal forums are more of a conversational layout and not flattened like traditional forums. You can look at my site in its infancy. I haven't had much time this week to work on it. http://starjax.com/
. I will caution that it takes a fair amount of experience at coding to creat and theme php-nuke. On the other hand there are some nice themes available for download.
SMF is open source as well. offers the ease of administration and setup like php-nuke but is more modern in it appearance than php-nuke. I found it to be very easy to use. In fact I know this is offered at GoDaddy.com, so if you want something cheap to play with until you figure out what you want, it may be worth a try.
There are several places where you can get free forums, but are limited to the customization you can do and to the forums they choose to run. On the other hand they are free.
Please let us know if you have any other questions.