First, are you a first time dog owner?
If so, you must take the SKN theory course BEFORE you acquire a dog. This is federal law.
First time owner is generally defined as having previously had a dog registered in your name in the ANIS database. This is clear cut for Swiss residents, but for a newcomer to Switzerland who has owned dogs (in his own name as an adult, a 'family dog' does not count) in another country the issue is less clear cut. In such cases you need to contact the cantonal Veterinäramt with proof of your previous ownership for a ruling on whether you must take the SKN Theory course, or not.
The decision is made on an individual basis.
A good Swiss breeder or shelter would not consider you if you have not sorted this out, as anyone who does not know the law - and of course comply - would be considered irresponsible, not a good candidate for one of their dogs. So before you go any further, make sure you have the SKN Theory course settled. Most will ask to see either your SKN Theory certificate or your letter of exemption.
Also be aware that all owers, first time or experienced, are required to do the SKN Practical course within 12 months of acquiring a dog. So start your research into that as well.
Additionally you will have to comply with cantonal law, where most dog control issues are legislated. In canton Zürich for a small dog - that is, under 15kg or 45cm - there are no additonal education requirements beyond the federal. Should you choose a dog larger than that, however, you would have a whole series of training classes to fulfill, puppy, adoliescent, and adult training - at specific times in the dog's life.
I know you said you are looking for a small dog, but... I own a dog whose breed clearly falls into the small category. Yet she kept growing and growing, she is far larger than the breed standard. So if we lived in ZH (we don't) she would actually fall under the List 1 training regs, despite the fact that her breed is classified differently.
Now as to your question on breeders.
Be aware that good breeders make sure that their pups go to people who are worthy of them. Which mean that it isn't simply a case of rocking up with a fist full of dollars expecting to take a puppy home - many have a selection process for potential buyers. You will need to contact breeders in the first instance, describe your family and your experience, talk about why you have chosen this breed and why you are interested in their pups. If what you write fits with the kind of family the breeder favors, you would be invited for an interview. The whole family will likely need to attend, children and other dogs included if you have them. (The behavior of small children around dogs, and the parents' ability to supervise them correctly, is something good breeders look into.)
Often good breeders plan well in advance, often keeping a waiting list of potential owners. The process of applying, interviewing, getting accepted for a waiting list, then finally bringing home your puppy may take months or years. Occasionally a good breeder has a pup available if someone on the waiting list for the current litter has backed out, but this is often the exception. So set your expectations accordingly.
Similarly any good Tierheim will want to see your SKN Theory documents before allowing you to adopt one of their rescue dogs, will expect you to introduce yourself, then invite you for an interview if you fit the dog's dossier, will want to assess your family's ability to meet the dog's needs.
All of the above, either from a good breeder or rescue, is done for the dogs' welfare. A good breeder or shelter wants to know that their dogs will be well cared for, for the dog's entire natural lifetime.
Any Swiss breeder or rescue who does not want to see your SKN documents is not a reputable breeder or rescue, and you should run, not walk, away. This is one of the first signs of a battery farmer or 'Hundehandler'. (Yes the 'Hundemafia' now pretend to be rescues as well as breeders. These vile folks are very active in Switzerland, too many poorly bred, sick, abused, mentally damaged dogs are being bred here or brought to Switzerland due to this nefarious trade. Please do not add to the problem by lining these evil bar stewards' pockets.)
As a side note: There have been several articles in the newspapers of the heartbreak of owners who disregarded the warning signs of the illegal dog trade. Illegally imported puppies without proper rabies vacs can be seized and euthanized. So naive owners buy a puppy from a dodgy source, lose their hearts to the little bundle of fur... and then heartbreak. I can't stress often enough: eyes wide when buying or adopting. Research the breeder or shelter carefully.
If you are set on a puppy from a breeder, start doing your research. The SKG is the Kennel Club in Switzerland, each individual breed club regulates their breeder members. Each breed club has a Zuchtwart, the person who collates information on current and planned litters. This is where you should start to find breeders.
I am worried that you are simply looking for 'a small dog'. Perhaps it's just the way you have worded your post, but it comes across as if you have not done enough research into the type of dog suited to your family and lifestyle, into the type of dog whose needs you can meet. The range of different characteristics among small breeds is huge - and thus 'small dog' is not enough to assess whether the fit between the dog and your family. And do remember that within a breed there will also be a wide variation of individual temperaments. Since you haven't even decided on a breed yet I won't give you links to the various breed clubs. Once you make that decision you can easily find them on the SKG website or by googling breed+club+Schweiz or by breed+Zuchter.
If you would consider a rescue the place to start looking is the Tierdatenbank, the Switzerland-wide database of homeless animals. You can search by many factors, including size. The database is here: http://www.tierdatenbank.ch/cms/tier...unschtier.html
But before you go any further, please research what owning a dog means in Switzerland, please research your obligations under both the federal and cantonal dog laws.
Three good threads you should read: How to spot a reputable breeder Adopting a pet from a Rescue Centre 3 scams, 2 rejects and a puppy
Federal dog law can be found on the MeinHeimtier website here: www.meinheimtier.ch
And Zürich law (as well as the other cantons) is summarized on the Tier Im recht website here: http://www.tierimrecht.org/de/tiersc...ht/zuerich.php
When you find your dog from a good breeder or shelter, you will be given a sales or adoption contract. Make sure you understand what you are agreeing to in buying or adopting the dog.
Please understand that taking on the responsibility of a dog is a 15+ year commitment, one that you must make knowing that whatever else goes on in your life, the needs of your dog must be a priority.
We have seen over and over again that too many expats are not responsible owners, taking on a dog on a whim and then abandoning their dog because he becomes 'inconvenient' when the next global opportunity arises. Unfortunately for the majority of expats who are indeed responsible, who place their dogs' welfare as a priority in making life decisions, the poor reputation of expat dog owners is becoming more and more widespread - and some breeders and rescues are wary of allowing an expat to adopt or buy one of their dogs.
So, as you go forward you might need to be prepared for extra grilling, be prepared to show how you will be able to meet your dog's needs no matter what happens in your life, where you end up, for the dog's entire natural life time. A good breeder or rescue wants to ensure that their dogs only go to people who are fully committed, who will give their dogs the best possible life.
Wishing you and your future friend all the best.