The BVet has this handly little site; plug in the appropriate info and it will tell you all you need to know to import a dog into Switzerland:
http://bvet.bytix.com/plus/dbr/default.aspx?lang=en
And you will need to understand the dog control laws in Solothurn; a summary can be found here:
http://www.tierimrecht.org/de/tiersc.../solothurn.php
Be aware that you will need to register your dog in the ANIS database within 10 days of arrival - only a vet can do this, so you'll want to make an appointment soon-ish. Also you need to register with your Gemeinde, pay the tax, etc.
Training classes (SKN) are now mandatory for Swiss-resident owners who aquired a dog after 1 Sept 2008; even if you are not required to take a class, I would strongly recommend that you do so. Dog ownership is viewed quite differently here in Switzerland than in many other places - the SKN classes may well help you avoid some of the difficulties dog owners accustomed to other norms have come up against. To find an SKN trainer in your area, the BVet has another handy app:
http://bvet.bytix.com/plus/trainer/
Hope you and your dog enjoy your time in Switzerland.
ETA: What breed(s) are your dogs?
Be aware that Solothurn has enacted BSL - restrictions apply to the following breeds and mixes: Bullterrier, Staffordshire Bull Terrier, American Staffordshire Terrier, American Pit Bull Terrier, Rottweiler, Dobermann, Dogo Argentino, Fila Brasileiro, and mixes thereof. If either of your dogs is one of these breeds, please consider the effect this move might have on them very carefully.