Use drill bits to cut the finger holes. The sizes of the drill bits used will depend on the size of the ocarina. Large ocarinas have bigger finger holes than small ocarinas.
Finger holes will add a very small amont of volume to the interior of the ocarina

Relative Finger Hole sises for 12 hole Ocarina
The size of the finger holes are relative to the size of the ocarina. The picture above doesn't give measurements, but it does show the approximate sizes of the finger holes in relation to each other and the ocarina. This first tuning is a "rough draft;" I always have to make adjustments when doing the final tuning. The numbers by the finger holes show the order in which they are uncovered to play the Major Scale. This is also the order in which they are cut, tested, and adjusted during tuning - from the lowest to the highest note.

These next two steps are optional. When playing the ocarina, I find it easier to cover the smaller finger holes if they are recessed. If you don't like the appearance, you can omit these steps.

With a finger nail, use a circular twisting motion to bevel the edge of the three (3) smallest finger holes.

Use the rounded end of a handle (I used the handle of tool #7) to press into the hollow made by your finger nail. A marble will also work well for this purpose. Doing this makes a uniform indentation for the fingers to rest in. This is not necessary for the larger finger holes; their size makes a good seat for the fingers covering them.