I think European Integration under the E.U. is a good demonstration model on how a global federal state could be created.
I don't know if the E.U. will endure or crumble, but it has done some great pioneering work in making a supranational federation. And I think this is where the future should go when it comes to global governance. I do remember stating that I would like more regional autonomy to create participatory motivation, but there are some matters that would still require global governance, which areas those are exactly is too tricky a question to answer with a simple musing, but dealing with crises areas and situations would be a top thought.
The E.U. defines itself in one way as an institution that secures the peace in Europe by promoting cross-border market integration. I think this would translate globally quite well. It remains to be seen how well the new Eastern member states can be brought up to level of their Western counterparts through E.U. policy and leadership, but just because that might not go so well doesn't mean that an institution such as the E.U. can not be the vessel of such change.
Maybe the U.N. can still be transformed into a global federation.