Re: Moving from Zurich to Geneva
Post 1
You have to cancel your residence in Zurich, then announce your arrival in Geneva.
Info (assuming you live in the city of Zurich...): http://www.stadt-zuerich.ch/prd/de/index/bevoelkerungsamt/personenmeldeamt/adressaenderungen/abmeldung.html
You have to go there in person, as I understand from the website.
Info for announcing your stay in Geneva: http://www.ge.ch/etrangers-confederes/fr/entree/welcome.asp?rubrique=changement-de-canton-ue-aele
The link contains the paper (I'm just assuming you're from EU - as you didn't give any other info...) that you and your employer have to sign and hand in for your change of canton - this can be done by post.