Coarsely crush the ice cubes, then fill 4 tall skinny drink glasses halfway full with the ice.
Add 1/4 cup mint leaves to each glass and, using a muddle stick or the handle of a wooden spoon, crush the mint leaves together with the ice (this is called "muddling").
Add 1/2 cup limoncello to each glass, and stir.
Add 1/4 cup of club soda to the top of each drink, and serve.
Note: on the show, Giada made her own limoncello from limes rather than from lemon, vodka, and simple syrup, with a week or marinating; if you can find a lime-based limoncello in the store, wonderful (we've only made it ourselves at home) - but otherwise you can use conventional limoncello.
Also, you could quarter a lime and put each quarter on the edge of the glasses, so that guests could add a squeeze of lime juice into their spritzer.