Tim,
There is a male thread on the end of the horn onto which the tip screws. I turn the collar for the thread on the lathe and then cut the thread with a die and a special alignment jig. I probably should report for the benefit of others that I turned, or attempted to turn, five tips for two horns. In one case, I had a section of tip so large, I could get two tips out of it and tried to do that by cutting it in half, lengthwise. I learned my lesson. The horn will de-laminate along the growth rings (if that is what you call it with horn) if you do that. In other words, the horn blanks shredded when I tried to turn them. A third tip cracked in the dye bath.
A staple holds the strap onto the base plug.
I will take more photos when I finish playing with the lighting. I have also contemplated shooting a 360 degree virtual reality view just for grins and giggles.