Almost everyone that I've taught how to crochet has somewhat panicked about how to know yarn from yarn. It's all in the labels, and eventually you won't even need them because you'll just be able to see and feel the difference!
First things first—A ball of yarn is also called a skein. Each skein should have a label on it that looks like this:
There are a few important things to know about on the label:
—The weight of the yarn (Medium, 4, Worsted)
—What the yarn is made of (100% Acrylic)
—Whether this yarn can be put in the washer/dyer or heat applied
—Recommended crochet hook size (and knitting needle size)
—And the dye lot (in this case there is none, but this becomes more important with more expensive hand-dyed yarns usually)
The arrow in the picture is pointing to the weight of the yarn, and is mainly what you'll want to pay attention to when you're getting started. It will tell you how thick or thin the yarn you're choosing is. Sometimes the nature of your project and instructions in your pattern will determine which weight of yarn to use. Other times, you'll find a skein that you love, and you look for something to make out of it. If you're adventurous you can experiment with making your own patterns!
But for now, here's a handy chart from Lion Brand Yarn that shows the different weights of yarn and what each one tends to look like.
What a colorful world! Even just viewing the pictures has been an enjoyment.