Although not an expert, the literature suggests to secure the horn from a kosher animal (preferably slaughtered in a kosher way). Kosher animals include: goat; ram; antelope; gazelle; Bighorn sheep; Ibex; (according to some this is the same as the wild goat)

A horn of a cow is pasul (forbidden) because  the golden cow was is connected with false worship  (And it came about, as soon as Moses came near the camp, that he saw the calf and the dancing; and Moses' anger burned, and he threw the tablets from his hands and shattered them at the foot of the mountain. Exodus 32:19)

Clear out the shell of the horn "keratin" by boiling of soaking in chemicals (In the journal of 'Biological Museum Methods' Vol. 1 Page 331 it mentions to boil the skull with horns for about 30 minutes and the horns should twist off, than scrap clean the inside, sprinkle with borax

Now the mouth-piece can be crafted.
In the case of a rams horn, once the cartilage is removed it needs to be shaped  to soften the horn use hot oil or by steaming and form into the tradition "j" shape, and by flattening the side.

To make the mouth piece.
The mouthpiece is the core of the Shofar’s effectiveness. Accordingly, much care should be devoted to its construction. First measure the hollow depth of the horn from the  opening. Line a bent wire along the outer length of the Shofar and record where the wire reaches from the opening of the horn. Measuring 1 1/2 inch or more (depending on the degree of curvature) from that mark towards the pointy tip of the horn, then designate where to cut off the tip of the Shofar with a coping saw. The cut must be perpendicular to the length of the Shofar. Once the pointy tip is cut of, a blunt flat surface results.

The mouthpiece is now created with a 3/16", 6 six inch long bit on a variable speed drill. Aim the drill in the centre of the flat end of the horn. Gradually the drill should be accelerated so that it cuts a narrow hole along the body of the Shofar until it penetrates into the hollow of the Shofar.

NOTE: if you use a drill at a sharp angle (not parallel to the body of the horn), you may cut the side of the horn, rendering the horn invalid for ritual use.

The Narrow hole that is created by the drill must be enlarged, tradition knife cut to create a conical or cup shaped hollow. The cone shaped opening helps ensure that a minimal volume of air can be forcefully blown through the canal with little effort and still resonate the Shofar sufficiently  to sound it clearly. The wider the canal, the easier it is to blow.

You will need to polish the mouth piece with a buffer of some sort.

Sources

"Historical Brass society newsletter Issue 7 pages 13/14
Title:           How to make a Shofar
Author:       Michale Albukerk

'Biological Museum Methods' Vol. 1 Page 331