Yesterday I used the link in your signature and got to the Webs site. Honest.
Now I'm not really sure what you're asking. The forums on the Splash Page of that site work fine and are remotely hosted. If your forums are remotely hosted like the ones on that Splash Page then you don't need to set up a MqSQL database on your server.
Maybe you're asking how to set up your own server on your own site (
http://achamo-torchic.brokenwishes.net/forums/) like that. It's not really necessary for you to do that since you already have a forum but you could. There's just a few steps you need to follow:
1.
Find a Forum Software Package. Google it. There's plenty of free ones out there.
2.
Read the documentation. Most Forum Packages come with precise step by step instructions on how to upload the needed files to your server, install them, and configure them including what needs to be done with MySQL if anything.
3.
Follow the Instructions. If you follow the instructions precisely you won't muck up the installation. Even if you do mess up you can just delete all of the associated files, upload a fresh set, and try to install it correctly again.