You asked

How often should my child's eyes be checked?

Your baby will have his first eye exam in the delivery room. His eyes will be examined for any signs of congenital eye problems. These are rare, but early diagnosis and treatment are important to your child’s development.
An antibiotic ointment or eye drops will be administered to prevent infection. Within a short period of time he will begin to focus on objects less than a foot away, such as mums face when nursing.
You should schedule your baby’s next eye exam when they are approximately six months of age. The optometrist will conduct a comprehensive eye exam and will test for visual acuity, excessive or unequal amounts of nearsightedness, farsightedness, and astigmatism. He will evaluate eye alignment, and examine how the eye works 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.
You should take your child for their next eye exam when they are between two and a half and three years of age. When they start school vision problems can cause learning difficulties so it is important to identify any issues as early as possible. 
You should schedule regular eye exams for your child or teenager as eyesight can change until he is in his mid twenties. 

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.