Not much to it. Just freeze your drink in a plastic cup.
You may use any freezable drink. Dairy products do not freeze and thaw well so avoid these.
Some juices will not completely freeze but will leave a syrupy sticky slime. These are best enjoyed when they are only partially frozen.
I often drink some of this icy drink, then replace it in the freezer to have more later.
My favorite drinks to chill/freeze are apple juice and lemonade.
WARNING: Do not use a glass container as it will break as the drink freezes. Also, paper cups tend to tear. By tilting the plastic cup during the chilling stage, there will be less stress on the cup as the fluid expands during freezing.