And you can share your new skin

At the Skindex at http://www.minecraftskins.com

For example, I just created one and uploaded it there an you can see it at:
http://www.minecraftskins.com/skin/71530

And here is what it looks like:
http://www.minecraftskins.com/preview/both/9/71530

It's a skin made entirely of dirt. DIRTMAN

Creating your own Minecraft Avatar Skin

Now that you know how to change your skin, you can create your own using one of many tools available to do so.
The one I used was SkinEdit available from here:
http://www.minecraftforum.net/viewtopic.php?t=4843

It's very easy to use and you can create whatever you'd like - takes a few tries to get it perfect but very fun.