Learning to ride a bicycle safely without training wheels is a rite of passage in childhood. Most children between the ages of 4 and 6 can develop this skill with some guidance from their parents.
The first step in teaching a child is to make certain that you have the correct equipment. The bicycle should be small enough and the seat adjusted low enough so that the child can sit on the seat with both feet flat on the ground. A properly fitting helmet is mandatory from the beginning. I recommend that the child wear thin gloves and have on long pants and a jacket to avoid some of the scrapes and scratches that may be part of the learning process.
Lessons should be carried out on a flat paved area with no traffic or other distractions. Teaching safety should be an integral part of teaching the actual skill of riding. Before attempting to ride, the child should be taught how to use the brakes on the bike, whether hand brakes or pedal brake.
The first step in learning to ride is to put both feet on the ground and propel the bike forward while learning to balance it. This should be done repeatedly for short distances using the feet to stop when desired. The next step is to put one foot on a pedal but to propel the bike with the foot that is on the ground while maintaining propel balance.
Once this has been accomplished, both feet should be put on the pedals and the child should use them to move the bike. Use of the hand brakes or pedal brake should be part of this too. Once he/she is able to pedal a short distance, it is only a matter of time and practice before this becomes a natural skill that improves quickly. At this point it is important to emphasize safety such as maintaining a proper speed and watching for obstacles.
It is always beneficial to have a reward in mind once the goal is achieved. A little ice cream or other treat can motivate a reluctant learner. There are numerous videos on YouTube if a visual demonstration would be helpful. The main things to remember are to teach safety and to make this a fun experience.