First of all, you need to keep the couple of Canaries in separate cages because keeping them in the same cage can cause harm as male Canaries are usually hot tempered and they can kill females.
Always put them in one cage when you observe that both male and female Canaries are ready to breed. Otherwise keep them in different cages in order to avoid any loss.
Keep observing the couple in order to know when they show sign of breeding. There are many signs that will let you know that both Canaries are ready to breed. When these Canaries get ready to breed they usually become a little harsh in their sounds or chirping and always drop their wings downwards while they chirp.
Dancing around in the cage is another sign that tells that both Canaries are ready to breed. Usually female Canaries start tearing the paper in the cage or their vents appear swollen and red. They also start raising their tails in order to get attention of the male Canaries.
When you observe the readiness from both sides then put both Canaries in the same cage. However, keep observing in order to take immediate removal of the male from the cage if it gets angry in order to protect the female.
Usually both Canaries get accustomed to each other if they are ready to breed. Let them spend more time together and usually they keep mating frequently.
You need to build or add a nest in the cage that you can purchase from any pet shop in your area. Remove the male Canary when the female starts sitting in the nest which means that she is ready to lay eggs.
Make sure that you provide appropriate food to the female canary when it is nesting. Give it small pieces of fruit and other feed containing rich seeds. It will help the Canary to produce healthy eggs.
Usually a female Canary lays up 5 to 8 eggs and these eggs require hatching for almost 14 days. Keep the small chicks together after coming out from eggs. Separate these little chicks in different cages when you see they start eating without the help of their mother.