I am taking my forums down now. So, I thought it would be better to take backup and keep files safe for the future. If required, I can run my forums again. I would like to know that I have downloaded complete forums folder from file manager till now. Do I have to do anything else?

You would need both the files and a database backup.

I have a now very old (May 2009!) guide, in fact afaik there's only one site with it still available. It is however mostly still correct. If you cannot access your web control panel (usually Cpanel although some hosts may have their own instead) contact them and ask. :)

http://community.invisionbyte.net/tutorials/article/82-taking-backups-with-cpanel/