You asked

What does a comprehensive eye exam involve?

When your baby reaches six months of age you will need to schedule a comprehensive eye exam. The optometrist will examine the family’s vision history. Using a penlight she will examine the outside of your baby’s eyes, including the eyelids and the eyeball, looking for discharge and other signs of infection, allergy, or blocked tear ducts. She will check the position of your baby’s eyes, lids, and lashes.
The optometrist will check your baby’s eye movement by watching his ability to fix on an object and follow it as she moves it into different positions. Each eye will be tested and then both eyes together.
To test your baby’s vision, she’ll watch how he follows an object with one eye and then with the other, covering one eye at a time. If your baby follows the object with one eye but not with the other, it’s a sign the vision is worse in that eye.
The optometrist will also observe the refraction of light to the back of the eyes. In a darkened room (to make the eyes dilate) she’ll use a lighted instrument called an ophthalmoscope to look for a red reflex in each eye and then both eyes together. This test will rule out eye diseases like cataracts.
The optometrist will test the eyes for visual acuity, excessive or unequal amounts of nearsightedness, farsightedness, and astigmatism. She will evaluate eye alignment, and examine how the eyes work together as a team. The general health of your baby’s eyes will be assessed as well. Problems are not common but it is vital to identify issues if there are any as early as possible. Vision problems, like amblyopia are easier to correct if they are detected early.

More questions

Children's eyes are sensitive so it is vital to protect them from the sun's harmful rays.
Your young child can have their eyes tested even if they can't read
Regular eye exams are essential in order to monitor your child's eyesight.
There are some signs to watch out for if you think your child may have a vision problem. 
Should your child get any kind of chemical in her eye you should treat it as an emergency and bring her to the hospital immediately.
You should take your child to their G.P. or to the hospital if you notice any of these symptoms. 
You should seek immediate medical attention if an object seems to be imbedded in your child's eye. 
If your child appears to have something in his eye you should seek immediate medical attention if it is imbedded in the eye. 
As your baby learns to crawl and begins to explore her surroundings you will need to child proof your house to prevent eye injuries.
Babies and young children are always getting up to all sorts of mischief and eye injuries are quite common. It is important to always consult with your G.P. should any eye injuries occur.