Bike safety may seem like common sense but there is a reason why the saying “Common sense is the least common thing in the world” is so popular. Though the basics of bike safety such as wearing a helmet or riding in the bike only lane are pretty well known the attention to details can mean all the difference between a serious bike injury or no bike injury at all.

Helmet How To's
Helmets are built to withstand impacts and protect the head from dangerous collisions. However, when used incorrectly helmets can also pose a danger to the wearer. There are a few crucial tips to make sure that in case of a fall the helmet functions exactly as it was designed to:
Bike helmets must be worn every time the child gets on the bike. It does not matter if they are going to ride for only ten minutes. The helmet must be worn.
The helmet must fit perfect. It should not be too tight or too small.
Having the right size is not enough. It needs to be worn properly as well. Many children tend to tip the helmet backwards to help them see better. This is incorrect as it exposes the forehead.
The straps must be fastened securely at all times. This does not mean that the child needs to feel strangled. It should be secure enough that it does not slip off with impact or speed.
Though helmets are made to withstand impact they should not be thrown around. This may cause damage to the outer surface making it unsafe to wear when it really matters.

Bicycle Helmet Safety Institute: A website dedicate purely to the safety of bicycles.
Helmet Best Practices: A guide to bicycle injury interventions.
Mandatory Bicycle Helmet Law in Western Australia: Guidelines to specific laws and resources for wearing a bicycle helmet safely.
Cycle Helmets: An overview to bicycle helmet safety.

Training Wheel Safety
Though training wheels may be one of the easiest ways to help children learn how to keep their balance on their bikes, there are a few things about them that could actually be more dangerous. Firstly, they are relatively high up as compared to starting with a tricycle and thus falling will still be a painful experience. Also, they make turning a little bit more challenging but at this stage children should not be turning sharply in the first place. Because children will feel relatively secure about training wheels they may be tempted to go faster than they can handle. Therefore, if the child is using training wheels make sure they are comfortable with the breaking process before they start to speed up.  

Learning to Bicycle without Pain, Teaching Bicycling without Strain: Teaching a kid (and adult) to ride a bicycle.
Teach Your Child How to Ride a Bike: Types on training wheels and helmet wearing for the first time rider.
Training Wheel Dangers: Being aware of the dangers and alternative to training wheels.

Traffic Skills
It may seem like traffic skills should be learnt when young adults are learning to drive but if a child is biking on any road even if it is not a major traffic zone, knowing the traffic rules will keep them safe. Start by teaching the basic rules such as the meaning of red, yellow and green lights. Signs such as crossings, yield, and train signals are also important. Teach them basic hands signals for turning and stopping. These can be exciting little tips which will keep your child interested and safe on the road.
Traffic Sign Answer Page for Kids: Excellent website dedicated to teaching children the meanings of traffic signals with animations.
How to Teach Children Road Safety Signs: Step by step instructions for teaching road safety to children.

Areas to Avoid While Riding
Make sure that the child knows where it is safe to ride and where it is not. Making a few trips with them in the neighborhood is also a good idea. Identify the busy roads to avoid, gravelly and rocky areas, and explain to them the dangers of wet leaves and large puddles. Make sure that they know that puddles are unpredictable and though they may be fun to ride through, there may be hidden dangers such as deep holes or large rocks.
How Not to Get Hit by Cars: Important lessons in bicycle safety.
Australian Cycling Forums: A forum where you can ask questions and get answers by cyclists in Australia.

Tips for Adults to Keep the Children Safe
There are a number of small tips which can help keep your child and those around you safe when riding their bikes. These tips start from the very day that children learn to ride their bikes to the time they are riding on their own.
When a child first learns to ride make sure they start off in an area which is completely obstacle free. Even small stones can throw a practicing child off balance and give them painful bruises and scrapes. Try going to a park away from trees, slides and swings. You can even go to an empty parking lot but make sure that no cars are expected around the time that you are teaching.

Start by having the child learn how to keep their balance. This is often easier achieved with a set of training wheels. If you don’t want to use training wheels you can always hold the seat from the back and run along until they are able to keep their balance. This second method almost always guarantees more falls and bruises but has its advantages as well.  
If a child refuses to wear their bike helmet try to make it more personal by providing permanent markers to decorate it. Making it a ‘cool’ helmet may make it more appealing.
Cycle Safety for Children: Numerous cycle safety tips for children.
Educating Children and Teens: Information for adults to provide children and teens for maintaining bike safety.

Further Resources

Teaching Kids to Ride: Detailed advice on various aspects of bike safety with children.
Helmet Related Statistics: Various information for incidents regarding bike safety.
Tips for Young Children: information for infants, babies, and kids for bicycle and tricycle safety.
Bike Safety: All about bike safety including where to ride, helmet safety, hand signals and much more.
Teach Your Chile Well: Bicycle safety issues.