Remember you are providing a learning service, not just training courses. Make sure that everyone in your support team is ready for the transition. It's important to provide an instant help facility for learners who get lost. So make sure the help content of your courses is useful, and make it clear to learners who they go to for additional help and how fast they can expect to receive it. If you are using your own help-desk folks, let them know what to expect, provide them with the opportunity to get to know the courses, and use your first batch of learners to document likely problems and solutions. Also develop a FAQ list that you can append to the courses. If you can, provide learners with a threaded forum like this one, where they can post non-urgent problems for you, a tech support person, or other learners to comment on.
If people are to learn at their desks, you might also want to do something about creating a more comfortable learning environment. Briefing managers to be supportive, and not interrupt learners, can help a lot. I have seen companies provide learners with a 'learning environment' kit that includes yellow crime-scene tape printed with 'learning taking place, do not cross' -- people can pin it across their doors or cube entrances to let others know that they are not available and would appreciate quiet.
Follow-through and getting feedback is important. If you are using a LMS or equivalent, track start and finish information. Follow up with learners who appear to have stalled or abandoned the training -- remembering that for many, completion is not their objective. And congratulate those who actually complete. Leverage enthusiasm where you find it -- a happy learner can do a lot to get others into the new mode of learning.