As a new SFDC user, I'm probably overlooking something obvious, but if SSO is enabled, how would I go about creating an API connection? I understand that I would need username, password, and security token, but in a Single Sign On situation where no password is required, what do I use as my password? And how can I receive a copy of my security token? Thank you.
If you can't log in because you have no password (either because it's SSO managed or delegated), you can't use the standard SOAP login call. Instead, the application must support OAuth authentication. The application will redirect to Salesforce, which in turn will redirect to the SSO provider, which after authentication redirects back to Salesforce, and then back to the application.
You can see this in the newest version of the Apex Data Loader. Go download a copy of it and try it out. When you first try to perform an operation, choose OAuth login, and on the login window, choose "log in to custom domain" to select your My Domain with SSO enabled. After completing the login, you'll be able to use it normally.