I have a cassette style wheel. How do I measure whether it will take a 7, 8, or 9 speed cassette?
I would go to a bike shop, or take some hub you already have.
As far as I know, there are only two sizes: one for 7 and one for 8/9/10 (these are the same, just the distance between the sprockets is progressively smaller to fit).
And if your data-processing capacity and confidence are good, you can dig some info here: