First here is a picture of two points I bought ,the small black one is from 3 Rivers and the larger and shorter one is from an jumi archery equipment dealer .
First I chuck up a horn tip in the lathe ,the point of the horn ,is the point's tip.
Then using a not so rough round rasp ,on the tool rest ,start rounding the horn.
Then with a triangle file shape the shoulder.
And refine the tang with a flat file.
It should come out of the lathe looking something like this.
Notice the piece of horn in the bottom of the above photo, it is shaped to fit in a three way chuck or a drill.
Now I cut off the flat base at the tang and do the final shaping on a sander.
There you go .I hope I didn't leave anything out.
Ralph