Just noticed this thread from a few months back.
C clefs are very much still in use; I ran into an amateur violist who got to college without ever being able to read treble or bass clef.
I used to teach ear-training at the college level and still teach new clefs to my students as part of what I do, even when the main focus is on playing an instrument.
Briefly, here is how I do it, which is how my teachers taught me:
Get a copy of "Complete Method for Rhythmical Articulation" by Pasquale Bona. The book is written entirely in treble clef, but the method is to pretend each exercise is in whatever clef you want to work on. If you don't want to buy the book, you can start with these selected exercises that I put into Sibelius and up on a web page
http://kbnj.com/bona.pdf
Always learn a new clef by saying, out loud, the name of the reference note and every note between the reference note and the note you're reading. E.g., if the note written is what would be middle C in treble clef, and you're trying to learn tenor clef (reference note is C on the 4th line of the staff), you say, out loud, C B A G F E D C B, because that note is a B in tenor clef. NB: I infinitely prefer to do this in solfege, so you'd say Do Si La Sol Fa Mi Re Do Si.
You progress by learning to name only the notes on lines and not every note, and you stick with that, so for the above example, Do La Fa Re Si (or C A F D B). If the note you're reading is above the reference line, you just read every note or only lines up instead of down, stopping at the note you're trying to read. E.g., what looks like a top-of-the-staff treble G would find you saying Do Mi Fa, or C E F because that's an F in tenor clef.
You progress further by treating all the notes between the reference note and your note as grace notes - you say them quickly, stopping on the note you're reading.
You progress further by doing the above at a slow tempo with a metronome, grace notes included and you try to gradually increase the speed.
You progress further by thinking the grace, in-between line names instead of saying them out loud and you try to gradually increase the speed.
Anywhere along the way, once you have begun using the metronome, you also add conducting. And your goal is to be able to conduct and say these exercises with a metronome and you try to gradually increase the speed.
It's worth stressing that you don't sing, you just speak. You're not trying to improve your ear here, and you're not trying to use your ear to help you perform a piece written in a new clef; you're trying to get better at reading a new clef, and the less you use your ear for that, the better and quicker you'll accomplish it.
NB: This isn't one of those things that harder to talk about than to do; it's rather the opposite. The principles are simple and clear but, like learning any new language, there's no substitute for time and energy spent in speaking it in order to acquire fluency.
Hope that's helpful to someone out there.
-S-