The process is simple: Just place some flavored syrup, club soda, and a little half and half in large glass filled with ice, stir gently, and sip the drink through a straw. The proportions will vary, depending on your taste. There are more complicated instructions on the Internet that will instruct you as to the order of ingredients, when and how much to stir, etc.
The fun begins when you discover a grocery store with a good variety of syrups. We found ours at Toucan Market in Las Cruces. So far, we've tried Torani Orgeat (almond) and Le Sirop de Monin Vanilla; but there are a lot more we'd like to experiment with--I remember seeing raspberry, amaretto, apricot, grenadine, pomegranate, butterscotch, chocolate almond, mango, hazelnut and lemon. There are lots of other flavors, as you will see when you visit the Monin site. You can use the syrups in a variety of tea, coffee, and smoothie concoctions, too.
Mix up your soda and sip it while sitting out on the patio in the desert winter sunshine. That's what we do!