We used to be able to retrieve our skins simply from http://s3.amazonaws.com/MinecraftSkins/***.png, unfortunately this no longer works, but I have an alternative. (All the other sites you see will be using this method too, just automated)
This tutorial will show you how to download your current minecraft skin, this will not show you how to retrieve old skins.
Note, this is overly complicated and there are much more simple alternatives, but I'm a wally so I like being awkward.
Retrieve your UUID, you can do this by any means you wish. I will give an example below.
a: Visit here and look for Look for your bunch of numbers that are in bold and copy it.