This is really a place where you would give each quote a pointer to a user object, and then you could just get the publisher of the quote without an extra query. But if you want to do it this way, you would do:
let query = PFUser.query()!
query.whereKey("objectId", equalTo: (quote["publisher"] as! String)) // You can unwrap it as long as you are sure that quote is not nil, and the publisher is set.
query.getFirstObjectInBackgroundWithBlock({ (user: PFObject?, error: NSError?) in
// check for errors and use the object
})
This way of doing it also creates Parse security issues, as anyone with your app's ID and key can get a full user list.