Only Administrators can assign Teacher rights. If you are logged-in as an Administrator, choose(click) 'Assign Teachers' from the Administration options (should appear in the relevant box to the bottom left of the Moodle front page). Choose the relevant course from the list and then select from the list of potential teachers which appears next. Potential teachers must have already registered on your Moodle or they wont appear on the list. To add the relevant person to the list of active teachers on that course, just click the little left arrow next to their name in the list and it will move from the 'Potential Teachers' list to the 'Existing Teachers' list. Presto! You have now added a teacher to a class.
Hope this helps.