I can just tell how I found my breeder.
Go to shows near you (travel distance possible for you as flying saint pups is not an easy task) and find which stud dog you like. For example, I have very personal likes/dislikes, but show titles just helps to find some quality on top of your own gut feeling (I'm sure this stage can be done on internet).
Then do the research on pedigree, and - most important - previous litters sired by dog that you like. (Great dog does not mean always that his /her children are great as well.)
Then - try to find parents and grandparents of the dog, and find out how are they now (HD test is important thing, but there are also ton of illneses that dogs can pass to offsprings, so if his father is already died from cancer as well as most of his littermates, I would not get any further on this dog).
Then go around to collect gossips about the dog you like, and his breeders... Stand close to judge table (or better, table where the club officials are sitting and keep ears on guard - you will be surprised how many things you can hear there!) and so on...
All gossips, bad or good, helps you to prepare for the right questions when you will be at that stage.
Then try to meet him and owners, talk with them, try to work out dog's personality and temperament and all that. Then find out has he had sired not so far away and any litter is expected, then repeat the whole research on the bitch that he has (or will) sired.
Or do the opposite and start with the bitch and work on the sire that she has been sired (or even better - will be sired).
For example, I like only full mask LH boys, so anyday now the boy that I like most, will sire the bitch that is owned by person, that I'm calling my breeder for nearly a year now. Then I will need to wait until I will know if the mating will take (the previous didn't) and then, when puppies will be born, another 2 weeks to see is there any LH boys in the litter.
The dog that I want to be father of my pup, has sired a dam already which I do not like (on top her HD score is D, not good at all)... So I better will wait and bite my nails
This is on top of basic research - all health tests to be done for at least few generations like hips, elbows, eyes and so on...
I would really start with confirmation/show rings to find what exactly I want to see in pup...
All this is because I want a possible show dog. For example, for my first saint many many years ago I had just one but very strong requirement - perfect temperament (I had small children at home and needed extremely friendly dog, without any possibility of beheivior issues, and I got one exactly that I wanted).
If you are looking for "just a perfect dog" and can afford the vet bills then rescue is an option as gut feeling is the only important thing
I have one resce at home now, complete foster failure, she is complete mess if we talk about breed quality, but such a sweetheart - all love, pure saint in heart!