Initial setup turned out to more challenging for many users than I had hoped. I am trying to counter that by providing detailed instructions that cover not just the happy path but also many of the issues users have ran into in the past. The recommended reading is longer than one might wish, but skipping it does not necessarily save time.
Forge uses the Ghub package to access the APIs of supported forges. How this works and how to create and store a token is documented in (ghub)Getting Started. Please read that in full before coming back here and continuing with the subsections listed below.
https://github.com/magit/forge/wiki lists additional resources; including a link to a much shorter quick-start guide provided by a user.