As it happens I have taught a course on Tolkien in the past and found that
Bethberry's advice is the best. Ask them questions about the text to get them engaged, and then direct their attention toward the relevant passages of the Appendices to get them looking there for the answers.
The key thing here, though, is to ask useful questions, not just "what parts of the novel do you think are cool?" Ask them things that will get them wondering about the thematic elements (things like, "Does Frodo 'fail' in his quest or not?" or "Are women important in the novel?" or "Why does Tolkien have all these songs and 'made-up' languages?") After the students have batted these issues around from within the context of the novel alone, you can work with them through the material in the Appendices that will help their understanding.
The key point that I always like to make about the Appendices is that they lead the reader past the 'end' of the book and help make the transition between the relatively 'closed' experience of reading a novel and the more 'open' experience that Middle-Earth has become. What is so interesting about the Apps is not what they do explain, but what they don't. The very fragmentary nature of so much of it leads our imaginations to wander and look past the covers of the book for answers.
Heck! You can even tell them about the Downs -- what are we doing here if not exploring the unanswered questions or interesting threads introduced in the Apps?
Finally, I think the really key thing to work through on the Apps is that Tolkien clearly felt that it was very important for his readers to have a sense that Middle-Earth is 'real' -- that it possesses a history and a cuture(s) and language(s) that exist 'outside' the book. The Apps are the main way he takes Middle-Earth and 'gives' it to the rest of us: it's not just his own place that he has created in his novel, its a world that is open for all to imagine and enter into: we can research its history and ponder its mysteries and learn its languages and debate its moral codes. If you can get your students thinking about why Tolkien wanted his book to end this way, you might find them becoming really engaged with what makes Middle-Earth work.
One Final Thought -- you might want to read Tolkien's fabulous essay "On Fairy-Stories". It's in the book
Tree and Leaf; in that essay he explains why it's so important that a 'fairy tale' be made to 'feel' (and even BE) 'real' -- which is what the Appendices are there to do!
Have fun with that class! I always LOVE teaching Tolkien!
