A good analogy for classes and objects: think of classes as cookie cutters, and objects as cookies.
With a gingerbread man cookie cutter (class), you can stamp out many gingerbread man cookies (objects). The cutter defines the initial shape of the gingerbread man - two arms, two legs, two heads. Each cookie, though, is its own entity. Bite off the arm of one cookie, and now it only has one arm. However, all the other cookies on the tray aren't affected - they still have two arms. And if you make a new cookie using the cutter, it will start out with two arms.
In AS 3 not all objects are made from classes. There are primitive types like int and Boolean and you can still make variables of those and just set them to True/False, 100/60.
You don't have to make your own classes really. You may have to use some classes that are part of the AS3 library, like Sprite, Font, Array, and Loader. For these you may have to use an import statement, but that's pretty easy. In the documentation at the top will be something that says "Package". Just stick a period on the end and the name of the class after that, and put "import" in front of that, and you have the import statement you need, like
import flash.display.Sprite; // "flash.display" is the package, "Sprite" is the class
Put that at the top of the first frame of code and you can use "Sprite" anywhere in the timeline.