Removing User Name with Admin Rights?

I haven't actually done this, but I believe you open System Preferences->Accounts, open the padlock if needed, select the account, and click the minus sign at the bottom of the list of accounts.

 

Do you just want to remove Admin privileges for that account or completely delete it?
You can delete the account as long as you're logged in as an admin, or you can select the user you want, click on Allow user to administrate this Computer, then delete the other admin account.