You should store your sparkling wines the same way you would your still wines, on their side, and in a wine fridge, if possible. If you have a wine fridge, store sparkling wine at a temperature of between 50 and 55 degrees.
If you don’t have a wine fridge, store your wine in the coolest location of your home, a basement, dark closet, etc., again, on its side. Then, when you are ready to drink the bubbly, pop it into the fridge an hour or two before opening in order to bring the wine to the perfect serving temperature.
What you want to avoid is storing the wine in a warm location because it can cook. Or in the fridge for too long, as frigid temperatures are also not good for the liquid, and standing the bottle straight up can cause the cork to dry out and allow oxygen to seep in.