If your web host is providing you with cpanel then you may be able to install a forum from there since it is automated. But if they dont the all you need to do is download the type of board you want to use then just follow the instructions. It isn't all so difficult. It is basically editing the config file. and changing permissions for files on the server.
I wouldn't advice to have the host install it automaticaly. The scripts they have in cpanel are always outdated. Get your hands on the latest release of the script you want to install and do it yourself. Running a forum will mean modding the theme and script afterwards, better learn everything from the start ;)
Their are many free forum hosts out their but you have to ask yourself these questions:
1). Do you want to move to your own server in the future?
If yes it may be cheaper to start of with a small hosting package or make sure that your free hoster allows forum 'dumps' for later on when you want to transfer all your members and posts across when you move to your own hosted server.
2). Make sure you check their Terms of Service (TOS) as one day you might try to login and find your forum no longer exisits due to 'violations' of TOS.
I personally would go for a host (does not need to be expensive) who can start you ouut with a small hosting package and increase it if needs be, also you want to buy a domain name but this is usally free if you sign up to a hosting account go to the forum software main website and download it from their, forum software these days is pretty easy to set up and basically does it for you.