Obviously you need ice to turn into snow. This isn't, unfortunately, as easy as it sounds. There are two kinds of machines you could use, and the type you have determines the ice you need. If your machine accepts ice cubes, you have it easy - you can make your own ice cubes or, in a pinch, pick up a bag of ice cubes at the supermarket. I've found that some shapes of ice work better than others: ice cubes from regular trays from my freezer don't work so well, but tiny cubical ice cubes from special small-cube trays work great. Rounded cubes that I might buy in bags of ice seem to be a mixed blessing... they work, but if they get in the machine at the wrong angle, they seem to get "stuck" not being shaved and I have to stop the machine and adjust them. Some machines require that ice be frozen in a special shaped mold, usually a cylindrical shape. My experience is that these machines make a finer, fluffier snow than machines that use cubes, but of course you have to remember to freeze the special ice or you can't make snow cones. Also, if you don't have enough molds, you may not be able to make enough snow for all of your guests. Further, this snow is so finely shaved that it tends to melt unusually quickly when you add syrup.
As I said above, the machines fall into the categories of those that use ice cubes and those that require special molded ice.
This is the machine I like best and use in my own kitchen. It uses ice cubes.
This machine uses molded ice or ice cubes.
Here's an excellent low-priced machine. It uses molded ice and is hand-cranked.
Here's another machine that looks nice.
When I'm home alone and just feel like having a snow cone, I often just use a small pyrex bowl. But, for guests and friends at parties, they usually enjoy it best in a cone cup.
Cone cups:
More cone cups:
Here's a kit of cones, straws, and syrup mix.
Here's another similar kit.
When you pour syrup onto your snow cone, remember that it will melt some of the snow. The finer the snow is shaved, the more it will melt. This is normal. As an alternative, you can freeze flavored drinks such as fruit juice or your favorite soda, and use no syrup on your flavored snow. This is a great way to cut calories, by using diet soda or sugar-free drink mixes.
You can buy syrups or you can make your own. Most people find it cheap and easy to buy them.
I have several packages of these and they're great for parties. It's a box of individual serving packets of flavor syrup. If you don't want to have a lot of bottles of syrup around, it's a great way to be able to have a variety of flavors anyway.
Here is an excellent strawberry-kiwi syrup. I use this brand of syrups.
Here is a selection of sugar-free syrups: