I know some people use hank and skein interchangeably, but the above is what I learned the different terms to mean.
If you buy yarn in a hank, you'll want to wind it up before working with it, otherwise you may end up with a huge tangled mess that will take hours and hours and hours to untangle - ask me how I know!
A swift and ball winder are useful, although not necessary. If you wind the yarn with a winder, you get a cake; if you use your hands, you'll get a ball.
In place of a swift, you can drape the hank over the back of a chair, your knees, your feet, or talk someone into holding it for you on their hands.
You can wind a center pull ball with a toilet paper tube or paper towel tube cut in half, here is a video.