In order to carve anything you must have the proper structure. That goes for faces, birds, fish, animals, etc. Imagine the eye. Basically it is a ball set in a hole covered with skin. Close your eyes and gently feel the structure of it. That is what you are going to try to recreate.
First, you must remember that a face is "five eyes wide". That means that there is an eye width from the side of the face to the outside corner of the eye. Then the eye itself and then an eye width between the eyes. Then the next eye and finally the last width from the outside corner of the eye to the side of the face. Divide your face into five equal vertical divisions.
Next, draw a horizontal line dividing the height of the face in half. In the 2nd and 4th divisions draw a ROUND circle making sure that the circles are divided equally by the horizontal line. This line will be the center of the eye.
On the inside corner (the side next to the nose) take a small #9 or #11 gouge, and following the bottom line, start about 1/3 of the way away from the corner and gouge the line out. Start shallow under the eye and deepen the cut as you get to the horizontal line. Next, from the top of the eye start about ¼ of the way up and make the same cut going deeper as you get closer to the horizontal line. Repeat these same steps for the outside corner of the eye. However, remember to cut the outside of the eye deeper than the inside because the eye wraps around the head. Between these cuts are the "eyeball".
Next, take a small #3, #4, or #5 gouge and round over the left and right sides of the eyeball. The eyeball should be completely round from left to right with NO flat spots. Redraw your horizontal line for the center of the eye.
Now we will cut the upper eyelid. Draw a SHORT line from the inside corner of the eye starting at the horizontal center line and draw it at about a 45 degree angle towards the center of the eye. This short line should go NO more than about ¼ of the width of the eye. Next, draw a line from the upper end of your short line to the outside corner of the eye. This should form the upper eyelid. Now, take a knife and undercut this line. You are making a stop cut for the next step.
Using a small shallow gouge, start at the bottom line of your original circle and cut upwards at about a 45 degree and then, continuing with the cut, cut up to your upper eyelid. Continue to make this same cut all of the way around the bottom of your eyeball starting from the bottom of your circle up to the eyelid. Make certain that you maintain the horizontal "roundness" of your eyeball as you do this. This will create the bottom of the eye socket in the skull and push the bottom of the eye back under the top of the eye.
Now, let's draw the bottom eyelid. This is done just exactly like the top EXCEPT that the lines will be turned upside down and the short line will start at OUTSIDE corner of the eye. Again, take your knife and cut along this line. Both eyelids should now be formed.
Now, let's cut the actual eyeball. Taking your knife in hand, make a short cut stop cut at top of both the inside and outside corners of the eye following the previous cuts for the upper lid. These cuts should extend NO MORE than ¼ of the width of the eyelid and should be deeper at the corners than at the center of the eye. Repeat the same steps for the bottom eyelid. These cuts should create a "V" cut at both the inside and the outside corners of the eye. A small, sharp pointed knife will make the next step a lot easier. Lay your knife flat on its side against the eyeball and make a "slicing" cut starting shallow at center side of you previous "V" cut and deepening the cut towards the bottom of the "V". If these cuts are done right, you should remove a small wedge of wood that will make the actual eyeball round.
LAST STEP: Take your knife and undercut the middle 1/3 of the upper eyelid fairly deep. Next, using a #8 or #9 gouge, make an angled cut in the middle of the eyeball upwards towards the line that you just cut with your knife. If this cut is done properly a half-mooned shaped piece of wood should pop out forming the pupil.
BEHOLD! An eye! Easy as that!
A NOTE TO REMEMBER:
When drawing your upper and lower eyelids, draw your lines so that it looks as though your eyes are squinting. When you actually cut the eyes, they will look more open than the way that you drew them. If, you draw them open, then it will look as though someone scared your carving.