These clefs are used, mostly, by strings, especially viola and cello parts, sometimes by the French horn (see the Brahms horn trio). If you have to play one of these parts on the piano, say to fill in for a missing cellist, just relate everything back to the middle C indicated by the arrow, as the diagram shows. It gets easier with practice, like everything. Just when you've got the part figured out, though, the cellist shows usually up and you're back to playing familiar bass and treble clefs.
An example of C clef use: Notice at the beginning the original C clefts are noted. The score has been rewritten in Treble and Bass clefs. [/youtube]An example of C clef use throughout the music:
The clefs started out as letter names written on the lines, and then those letters got fancier. They look fancy but the idea is really simple. Where everything comes together in the middle of the C clef, that is your middle C. Whatever line that is becomes middle C. The line below that will be the A line that you normally see at the top of the bass staff. The line above it will be the E line that you normally see at the bottom of the treble staff. And so on.
I got it. No need to post again otherwise my mind would be jumbled up again!