The most common login problem is from bookmarking the login page. This will cause future logins to fail as Blackboard checks the address used to invoke it. If that address is not "https://nmt.blackboard.com/" it will fail.
Most of the remaining problems are login failures. Your account name will be the same as your TCC account name, and your password will be the same as your TCC password. If your TCC password does not work it may need to be re-synced with the Kerberos system. To do that have the person visit the TCC web page ("https://tcc.nmt.edu/") and change their password. I think you can set the new password to the current one (if not you can set it to a temporary one and then change that to your current one) so that you keep your current password. (If that fails you can contact the Help Desk at 575/835-5437.)
The next largest cause of problems with using Blackboard is accessing it with a non-certified / non-compatible browser. To see if your browser is compliant click the "Check browser" link on the entry page for Blackboard.
While the pop-up windows about browser compatibility can be annoying they are important. Information about compatible browsers, and fixing browser problems, can be found at Blackboard's Browser Tune-Up page.
If you encounter problems with any of Blackboard's functionality you should run a Browser Check on your browser, and then follow the link (above) about browser compatibility to verify your browser's compatibility. If your browser is not certified you may experience problems even though it may be listed by Blackboard as compatible. The only, Blackboard approved, way around a browser problem is to use a certified browser.