Canaries nest in an open type nest, these are available for a few pence from the petshop.
They are plastic so you need to glue a piece of jute, carpet underfelt, or the shop will sell you that too, to stop the nesting material from moving all about and indeed, falling out. Give the birds some dried grass, pieces of fluffy wool (no longer than 4" or the legs may get caught). To finish the nest they like some feathers, small narrow paper strips or any soft small pieces of material.
Once the 4 or so eggs have been laid you can expect babies in 14 days, providing you have a cock bird included in the cage ofcourse.
To aid the birds with rearing the young get some rearing food from the shop and if you like add some hard boil egg. Feed as much as they will eat up in 4 hours.
Babies will leave the nest in 21 days and will be fed by the parent for another 14 days and by that time they will have made a new nest if the opportunity is there.
Hope you try it, it is great fun and, because they are cupnest breeders, you can see most of the process, although resist the temptation to shoo her of the nest, they come off quite frequently to void and eat.