We did a batch once the simplest way. From generic white grocery store table grapes, no less. We fermented the wine by the standard method, waiting for it to clear. I do not recall if we added sorbate but I do not think so; I think we simply bottles as-is and added a primer scoop of sugar. The amount escapes me, it has been a good 10 years, but there are places you can look that up. The sugar was added and then we capped with standard beer caps -- these work on standard champagne bottles, which we had saved up for this purpose.
I won't say it was spectacular, but it was as good as your general, average priced champagne. I would do it again and probably will when I have extra grapes. Yes there is a little yeast in the bottom, but you have to go with the more complex inversion technique to avoid that.