Updating a module is very simple, go to download page on Dotnetnuke.com look to min. Version the last release the module have and download it. make sure your DNN Version have the min. Version how it is reported in the download section. Log in as host to your DNN instance go to module devinations in system and upload the the new zip file. Check the update log for errors. If you have errors please post in this Forum.
About your error, I am not sure on what Forum version you asking. On Forum 4.4.3 we known on some upgrade issues on some instances by a not running Iugradable and some issues with the Lists table. For the last there is a pinned thread in this forum to fix it. Shall you run in a Iupgardeable issue there must be some manuell change on he database and perhaps a rerunning of the iUpgradeable (needs code changes). (There is also a post in this Forum).
Personaly I would suggest if you not on DNN 4.8.4 yet and you are before 4.6.0 make the Forum upgrade first and then upgrade the DNN. A upgrade of the Forum Module on DNN 3.x is not supported.