Usually, owners that are open to new members will write how you can send a request in the board description. If there’s no explanation or description in the group board, that likely means it is closed for collaborators.
When the group description says: “Comment on the board “Add me” to request an invite.”, you can simply comment “Add me” on a pin in the group board that was created by the group owner.
Note: If you do many messages in a short period of time (especially when they include links including that pointing to your profile or website), this can trigger Pinterest spam detection and get your account blocked or suspended. In case this happened to you, see this article on what to do when your account gets suspended.