One-Click Publishing requires that you have an account at shinywhitebox. We use this to track your usage of the service. You can login to your account here: My Account
This is the same email/password combination you used when you first purchased the product.
Normally, sign in isn't required because it's all saved for you as part of the registration process. So if you are not prompted to sign in, don't worry - that's intentional. We wanted to make it as simple as possible.
If you've purchased iShowU/iShowU HD after about August 2010 then it's quite likely that you will not be prompted to sign in.
Here's what you'll be presented with if you need to sign in:

This will be the case if: