The trompette de chasse is a hunting horn which has no valves (thus making it a "natural" horn). This means that any change of note can only be done by changing the embouchere (the shape of the lips) and the force with which you blow - although some additional note can be found by pushing your spare hand in the bell (the big horn bit). The basic notes obtainable are all harmonics of the natural tuned length of the tube. (For more info on harmonics in a tube, read this).
Trompette players all learn in the traditional way - from a member of the family or a friend. There is no formal lesson structure, so all players play slightly differently. Also, the tunes are not written down - so they are passed, along with technique, from generation to generation. The tunes do not fall into the standard western (classical) tradition of harmony or timing, so this makes the calls sound ancient and slightly foreign.
None of the tunes are very long - about 20-30 seconds, and then they all stop to discuss what is going to happen next. This is in the fine tradition of brass players everywhere, who like to stop for wine or beer as often as possible.
There is a Trompette de Chasse concert at Boussay Chateau in July. If I can organise myself sufficiently I would enjoy seeing that.
(thanks to Henri Proust for a lot of this info. He knows his brass!)