have a new Laptop with Windows 8 and have created a number of user accounts. Now I want to delete a couple of these user accounts and I can not find any documentation on how to accomplish this task.

Let us start with few questions-
1) Does your user account have administrator privileges?
2) Are you trying to delete a local or a Microsoft account?

I would like more information regarding the issue.
You can only delete another account provided your account has administrator privileges.

Method –
I would have you perform the steps-
a) Login to your default account.
b) Click on the “Windows logo” and type “User Accounts”.
c) Now, select “Settings” and then select the “User Accounts” icon.
d) Click on “Manage another account” and then select the user account that you want to delete.
e) Click on “delete the account”.
f) Depending on whether you want to “Keep the files” or “delete the files” choose the appropriate option.
g) You can delete the other accounts similarly.

Note: Once deleted, the user accounts cannot be recovered. Make sure you back up any data if required.