I have an iCloud account that I can access directly (web or iPhone), but my iMac only allows access to MobileMe in System Preferences.

If I log into MobilMe through System Preferences, I get an error stating that my password or ID is incorrect, but if I select 'Learn More' I am redirected to the MobileMe site where I can log in with my Apple ID and password. From there I can select to be directed to iCloud. How do I get the iCloud link into System Preferences?

You don't.
You log onto iCloud.com through Safari/web browser.

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