First you need to understand that dog law functions at three different levels: federal, canton, commune. So to answer your question fully we need to know where you will be living.
Without that info, the best I can do is give you an overview. So here goes:
Animal welfare is the competency of the federal government. The laws most referred to are SR 455, the Tierschutzgesetz and SR455.1, the Tierschutzverordnung. (In German - French and Italian as applies.) Regs surrounding dogs are mostly found in the TSchV Articles 68-79.
Text here: http://www.admin.ch/opc/de/classifie...796/index.html http://www.admin.ch/opc/de/classifie...103/index.html
Under these laws dog owners are required (among other things) to take a set of classes, the Sachkundenachweis. This applies to all owners of a dog born after 1 Sept 2008.
There are two SKN classes, the Theory and Practical.
The Theory class is required of all first time dog owners, and must be done before
acquiring the dog. Foreigners who move to Switzerland with their dogs should contact the cantonal Veterinäramt for a ruling on whether they will be excused from the theory class, or not. (Some are, some are not.) As an aside - even if excused, I strongly recommend taking the class as it is a good (read: IMO necessary) introduction to dog ownership here. Please understand that attitudes towards dogs here might be very different from what you encountered at home.
The Practical course is required of all dog owners, regardless of experience, and must be done with each and every dog acquired after 1 Sept 2008. You have 12 months from the date of acquisition to compete the course. (I have done the course 3 times now, with each dog I adopted after Sept 2008.)
Other federal rules:
Docking and cropping is banned. Microchipping and registration in the national database is required. The federal regs cover importation into Switzerland. Specific welfare issues such as space in kennels, social contact, use of pain-inducing appliance, etc. are covered in the federal legislation, as well as issues around abusive breeding practices.
Also, federal legislation regulates dog carers who work for pay. Keep this in mind when hiring a dog sitter.
Now the nuts and bolts of ownership responsibility is regulated at the cantonal level.
Because we do not know where you will be living, I can only point you to the summary put together by TIer Im Recht, click on the canton for specifics, a link to the canton's dog law is at the top of each page: http://www.tierimrecht.org/de/tiersc...echt/index.php
If you have questions contact the cantonal Veterinäramt.
Be aware that the cantonal regulations vary widely, from Zug the most laissez-faire canton, to (arguably) Zürich and Geneva, each more restrictive but in different ways. About half the cantons have some form of BSL in force - fortunately for you none restrict border collies as a breed so you are in the clear provided you follow local law. However, in Zürich (for instance) your border collies are on the 'potentially dangerous' list due to their size - any dog over 15kg or 45cm is considered List 1, and additional training classes are required.
But where and when your dog needs to be leashed, the annual dog tax, liability insurance, fines and measures available to enforcement, etc. are all cantonal matters - with very different laws.
In addition to cantonal law, there will also be local regulations. These often include places a dog is forbidden or must be leashed, quiet hours, fines for not picking up, etc. The local community is also responsible for collection of the annual dog tax. Local registration is also required in most places, in addition to the federal ANIS database.
One thing you will quickly learn about Switzerland is that in this Land Of Many Laws there actually is no rule of law, only rule of the local authority's interpretation of the law - and enforcement is often inconsistent.
So... while the good citizens of one community may have their binoculars trained on their neighbor's dog, trigger finger ready to report any infraction, you may find that the more easy going folk down the road take 'leben und lass leben' as their motto. And you might find that the Powers That Be take more rigid or relaxed approach towards enforcement in one community than in another.
In Switzerland - everything
But in most communities, do be aware that if you are the subject of a complaint be prepared to have things previously overlooked acted upon.
One 'cultural' issue that many foreigners struggle with here is the importance placed on quiet - barking is often what sets neighbors against you. So if your dogs are barkers you will need to start working on that, and to be aware of when official quiet hours start and stop in your commune. Be very sensitive to noise concerns - starting out with this in mind will likely go a long way to establishing good relations with your neighbors.
I advise all dog owners to understand the various laws in their areas, and to follow them at all times. It's simply a matter of being polite and respectful of others.
Switzerland is a very small overcrowded country. Most of us must live squashed together with little private space, every action impacts someone else - something dog owners must keep in mind at all times. 10 years ago we went through a wave of anti-dog campaigning where feelings ran very high - the regulations above are largely a result of that time. I hope those times do not return - and the best way to keep another anti-dog campaign at bay is to know and follow the law, to be a polite and responsible dog owner.
So - once we know where you will be living we can give more detail.
All the best to you and your dogs with this move.