The most common advice given to expats and immigrants is to learn the local language. Nothing else will make you feel at home like the ability to understand and talk to locals.
In the German-speaking part of Switzerland, if you’re starting from scratch it’s best to first learn High German (aka Standard German), and then learn the quirkier Swiss German. Learning High German first will teach you grammar, plus will enable you to read newspapers and understand official announcements. Many Swiss speak High German too, so you’ll be able to use it in conversation right away. After getting comfortable with German, learning Swiss German will allow you to understand the conversations going on around you.
If you’re serious about learning German (or any language), it’s a good idea to learn in many ways: taking a class, watching TV, creating flash cards, buying language-learning software, and using audio CDs, etc.
I’ve tried a couple audio CDs, and I ended up really liking the Pimsleur prooducts. Dr. Paul Pimsleur devoted his life to language teaching, and Pimsleur CDs use a very effective method of memorization that makes what you learn really “stick”. I’ve bought the full set of German I and II CDs and have been happily using them for over a year, but I realize they aren’t for everyone. For one thing, they’re kind of expensive. Plus they do not “teach it all”. You won’t be able to buy the Pimsleur CDs and learn German from them alone, but what they teach, they teach well. This review on Amazon does a great job of describing them in more detail.
Besides memorization methods, I also like how Pimsleur CDs teach pronunciation. For example, lesson 1 devotes time to teaching the pronunciation of the “ch” sound in “ich”, which has no equivalent sound in English. Their trick is to start with the English word “hue” and then take it from there, and it really worked for me.
One more piece of advice: if you buy Pimsleur CDs, buy them from someplace reputable like Amazon. I’ve seen complaints about some Pimsleur-named websites. Paul Pimsleur died in 1976 and these sites are not affiliated with him, so use common sense with online vendors.
Disclosure: I have no marketing, advertising, or business connections to Pimsleur or Amazon. I’m recommending Pimsleur German I and II because I bought them myself from Amazon (US), and I like them. Your mileage may vary.