If you just want to run a forum, you'd be better searching for ready made forum software and learning some HTML / CSS to tweak it to your needs.
If you really want to build one, you'd have to start by learning PHP and a database system - MySQL as you mentioned is a common one. For learning PHP, I point people at PHP The Right Way. I'm not sure of any standout resources for learning MySQL, you'll have to search for that yourself.
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