You can do that just with "regular" wine yeast. You'll need either champagne bottles and a champagne bottle corker, or you could do it in beer bottles with caps. Regular wine bottles aren't designed to hold pressure.
The difference between commercial champagne and just priming a couple of bottles will be that the homemade version will have sediment in it. Commercial (and some home) champagne makers is that they turn the bottle upside down, let the sediment fall to the top and then disgorge the crud before recapping. I don't know how to do it, and I think just doing it in a couple bottles is fine, if you don't mind some sediment in your sparkling wine.
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