Here is a
good picture of an ivory billiard ball from Deno Andrews' site.
There are several features clearly visible that are typical of used ivory balls:
1. The generally circular pattern of cracks formed from small scalloppy cracks. These fill with chalk and are dark blue.
2. The small dot in the center of the circular pattern. This is often in an uncracked region as is the case in the picture. This is the center of the tusk and is referred to as the "nerve canal." On carom balls, one of the cue balls was marked with two black dots, and that was done by inlaying some kind of black material into a hole drilled at the nerve canal.
3. The fainter cross-hatch pattern especially visible at the top of the ball in the uncracked regions. This is the grain of the ivory. It is very good indicator that a ball is ivory, especially if the ball is unused.
4. Radial cracks -- that is cracks at right angles to the generally circular pattern.
Another test is to touch the surface with a red-hot pin. Ivory will produce a burnt-hair smell. You will get a similar smell if you are playing with an ivory ball and miscue, but you have to smell the miscue spot quickly. You may get some funny looks if you are not alone when smelling the balls.