Most serious canary fanciers accept that the quickest way to establish a winning stud, which can in turn produce high quality young, is by line breeding.
If you take the example of a new fancier entering the hobby, most established breeders recommend starting with a minimum of two pairs of birds.
Ideally these have all been obtained from the same breeders, and so are already related, at least distantly.
When line breeding, the important thing is to remove any foreign genes, so that more predictable results are obtained, and you can realistically work at improving your stock during progressive breeding seasons.
The question is, How to go about it ? Have a look at a 3 [Three] Year example to get you thinking.